# JP4 SOLVING INEQUALITIES

This eighth grade mathematics lesson focuses on equations that are inequalities. It is the seventh lesson in a sequence of eight on this topic. The lesson is 50 minutes in duration. There are 34 students in the class.

Time | Caption |
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00:00:08 | Onegaishimasu. |

00:00:09 | Onegaishimasu. |

00:00:10 | Okay. Onegaishimasu. |

00:00:15 | Okay, we're going to start our homework answer comparisons |

00:00:18 | so, please take out handout number nine. |

00:00:20 | Now I'll have you write it. Please write, right? |

00:00:24 | Okay, it's this row. |

00:00:25 | One, two, three, four, five, six. |

00:00:28 | Okay, then please write it. Okay. |

00:00:45 | Okay, go ahead. |

00:00:51 | Go ahead. Please write it. Okay. |

00:01:16 | I'm going to check it so those of you |

00:01:18 | who haven't done it, |

00:01:21 | please hurry and do it, okay? |

00:01:29 | This... then. |

00:01:47 | I will hold this microphone... and walk around. |

00:01:50 | Okay. |

00:01:51 | Okay, then I'm going to check it |

00:01:53 | so please show it to me, okay? Okay. |

00:01:55 | Okay. Oh, great. |

00:01:58 | Everyone did their homework today |

00:02:00 | because we're going to be on TV. |

00:02:02 | Did you copy it? |

00:02:06 | Just one person... |

00:02:09 | just one person is a little different. |

00:02:12 | Arai! |

00:02:13 | This child... has forgotten his homework. |

00:02:22 | Please show it to me. |

00:02:23 | Bancho, you could do it by yourself, right? |

00:02:25 | Chino? |

00:02:26 | Are you feeling better now? |

00:02:28 | Okay. That's fine. |

00:02:33 | Okay, go ahead. |

00:02:38 | Arai, please hurry and write it. |

00:02:41 | It's only you, Arai. |

00:03:11 | Okay. Okay, then I had you write six so... |

00:03:15 | We'll compare answers together and verify them. |

00:03:18 | Okay, number one. |

00:03:20 | You exchange it and two X is less than 14. |

00:03:23 | We divide both sides by two, |

00:03:26 | so the inequality is X is less than seven. |

00:03:29 | Number two. Transpose and |

00:03:31 | negative five X is less than negative 10. |

00:03:35 | Then you're dividing both sides by negative five |

00:03:39 | so X is greater than or equal to negative two. |

00:03:43 | Okay, then the third one. |

00:03:46 | Date, please interpret this. |

00:03:52 | Multiply all with 10. |

00:03:54 | Oh, you mean you multiplied 10, right? |

00:03:58 | Okay. Ten- line up all of the head numbers |

00:04:00 | and multiply them by 10, |

00:04:02 | and 12 X minus four X is, |

00:04:04 | it's already like this, right? Okay. |

00:04:05 | Six and then 42. |

00:04:06 | If you organize them like this, |

00:04:08 | eight X is less than 48 and |

00:04:11 | X is less than negative six. |

00:04:13 | And number four is... |

00:04:15 | take off the brackets and |

00:04:17 | three X plus 12 is greater than five X plus two. |

00:04:19 | Then you transpose, and |

00:04:20 | negative two X is less than minus 10 and�when |

00:04:22 | you divide both sides |

00:04:24 | what is wrong at this point? |

00:04:29 | Where is it wrong here? |

00:04:31 | If I told you to correct it... |

00:04:33 | where would you correct it? |

00:04:39 | Eguchi, here... where should you correct it? |

00:04:41 | How would you fix this? |

00:04:43 | Number three and number nine. |

00:04:45 | That problem is wrong. |

00:04:50 | Teacher. |

00:04:57 | Now it's okay, isn't it? |

00:04:58 | Yes. |

00:05:00 | Okay. Then how about this? |

00:05:02 | Oh, negative two X. |

00:05:04 | Yeah. At the negative two |

00:05:05 | the inequality sign doesn't change yet. |

00:05:07 | It's okay as it is. And |

00:05:08 | when you divide it on both sides |

00:05:09 | by negative two then the direction is changed |

00:05:11 | to the opposite and X is less than five. Right? |

00:05:13 | Huh? It doesn't change when it became negative two? |

00:05:15 | Even if you combine like terms |

00:05:17 | there is nothing that can change the inequality sign |

00:05:20 | so just moving this one thing won't change it. |

00:05:23 | This is written, so, this is here. |

00:05:25 | So because this is here, its only at this point |

00:05:27 | you change the direction, you know. |

00:05:29 | You don't change it at the negative two part? |

00:05:31 | Right. You don't change it at this point. |

00:05:32 | You change the direction while you |

00:05:33 | divide both sides with this denominator, you know. |

00:05:35 | I didn't change it like that. Because this- |

00:05:37 | this changes it to negative two. |

00:05:39 | Because you do it with this. |

00:05:40 | Write it like this and... |

00:05:42 | I was too lazy to write that at the bottom. |

00:05:44 | People who write it like this are okay. |

00:05:46 | This corresponds. This is fine. Yes. |

00:05:47 | It's just that there's this line and this line but... |

00:05:49 | okay. Then number five. The brackets are removed. |

00:05:52 | Negative six X is less than negative seven. |

00:05:55 | Were there any strange points when you were doing it? |

00:05:57 | Why does it end up as this kind of fraction? |

00:05:59 | X greater than or equal to seven sixths? |

00:06:01 | Correct. |

00:06:02 | Okay, this is fine. |

00:06:03 | There was one that became a fraction, right? |

00:06:05 | Then the sixth one. |

00:06:06 | It seems like it was multiplied by 10 |

00:06:08 | and was all calculated, but... |

00:06:09 | You need to multiply 10 to this two as well |

00:06:11 | and make it 20, so... |

00:06:12 | Please be careful here because you may forget to write this. |

00:06:15 | Then 13 X is greater than negative 13 and... |

00:06:18 | X is greater than negative one. |

00:06:21 | Then... four or more correct is good. |

00:06:24 | It's a passing mark. |

00:06:27 | Then...people who could do four or more. |

00:06:29 | You are paper, okay? |

00:06:31 | Then people who did less than four are rock, okay? |

00:06:34 | One, two, and three! |

00:06:38 | People who had four or more are paper, you know. |

00:06:39 | People below four are rock. |

00:06:41 | Arai has zero, right? |

00:06:42 | Yes. It seems like everyone other than Arai is okay. |

00:06:46 | Arai. |

00:06:48 | Let's do our homework from now on, okay? |

00:06:54 | Huh? |

00:06:56 | Okay. That's what it's about. |

00:06:58 | Okay, then today will be the |

00:07:01 | final part of the sentence problems so, then... |

00:07:05 | I will have everyone use their heads and |

00:07:07 | think a little, okay? |

00:07:10 | Until now we've just done calculation practice, |

00:07:12 | but today we will have to use your heads a little so... |

00:07:15 | I'm asking you to use thinking methods. |

00:07:16 | How to think and how to look for it and |

00:07:18 | think about it may be a little difficult you know. |

00:07:20 | More difficult than just simply calculating, that is. Right? |

00:07:23 | Well then we'll go ahead. |

00:07:25 | Okay. Well then... please look at... the problem. |

00:07:31 | Fukuda, can you see it? |

00:07:32 | Yes? |

00:07:33 | Can you see? |

00:07:34 | I can see. |

00:07:35 | You can see. Okay. Then, Genji. |

00:07:40 | Please read the problem... in English. |

00:07:43 | [ BB: Problem 3. You would like to buy 10 cakes all together for less than 2,100 yen. ] |

00:07:44 | [ BB:One type of cake is 230 yen each and the other cakes are 200 yen each. ] |

00:07:45 | Okay. Genji, please read the problem. |

00:07:48 | You would like to buy 10 cakes all together |

00:07:51 | for less than 2,100 yen. |

00:07:54 | One type of cake is 230 yen each |

00:07:57 | and the other cakes are 200 yen each. |

00:07:59 | Yes. |

00:08:00 | Do you understand the meaning of the problem? |

00:08:04 | Arai, do you understand what this problem means? |

00:08:07 | You have 230-yen cakes and 200-yen cakes, right? |

00:08:10 | The 230-yen cakes are a bit more expensive. |

00:08:12 | And... you have 10 family members. |

00:08:15 | You want to buy cakes for each person. |

00:08:18 | But, I have only 2,100 yen. |

00:08:22 | Which cake... seems more delicious? |

00:08:26 | The 230-yen one. |

00:08:28 | The more expensive one is somehow more desirable, right? |

00:08:30 | And so... you want to buy as many |

00:08:33 | expensive cakes... as you can, |

00:08:36 | but what's the maximum that you can buy? |

00:08:41 | That's the problem. |

00:08:44 | Understand? |

00:08:45 | [ BB: If you want to buy as many 230-yen cakes as possible, what is the maximum number that you can buy? ] |

00:08:46 | There are cakes that are 230 yen and 200 yen. |

00:08:49 | You only have 210 yen. |

00:08:51 | But you need to buy 10. |

00:08:54 | But the 230-yen one looks more delicious |

00:08:57 | so you want to buy as many as possible. |

00:08:59 | Nine. |

00:09:00 | But you only have 2,100 yen, so... |

00:09:02 | so in fact how many 230-yen cakes can you buy? |

00:09:07 | Nine. |

00:09:08 | So today I am going to have you think about |

00:09:11 | how to find the answer. |

00:09:15 | So now I will pass out paper, |

00:09:17 | so please try and think about it. |

00:09:20 | See, you can do it if you do it like this. |

00:09:22 | See, you can understand- solve it if you do it like this. |

00:09:24 | I will present the problem in this way, okay? |

00:09:26 | Use the back, too. Four, five, six. |

00:09:30 | Two, three, four, five, six. |

00:09:32 | I didn't pass out the papers so... four, five, six, here. |

00:09:35 | One, two, three, four, five, here. |

00:09:38 | One, two, three, four, five, six. |

00:09:42 | Three, four, five, six. Okay. |

00:09:45 | I don't care about what kind of method you use |

00:09:47 | so please think about if you do this, you can buy 230-yen cakes. |

00:09:50 | Think about how many you could buy and how to figure it out. |

00:09:54 | Do we solve this problem? |

00:09:56 | This problem is for ninth graders, |

00:09:58 | so you can't solve it, so please use the back. |

00:10:00 | Please use back of the paper and think about it a little. |

00:10:03 | What do you need to do in order to buy 230-yen cakes |

00:10:06 | and up to how many can you buy and bring home? |

00:10:09 | Please think about this for a while. |

00:10:13 | It's good if you come up with an answer, |

00:10:15 | but please think about what you need to know |

00:10:18 | about how many to buy. |

00:10:20 | Well, we have about three minutes so it's okay |

00:10:22 | if you do it while you write notes there. |

00:10:23 | So, think about what you need to do to |

00:10:25 | find out how many you can buy |

00:10:28 | and find the answer. Okay, get started. |

00:10:31 | Please work by yourself at first, okay? |

00:10:34 | If you were in front of the store and you only had 210 yen |

00:10:37 | and you had to buy 10. What should you do? |

00:10:39 | Think about the time that you were in front of the store. |

00:10:40 | What would you do? |

00:10:45 | What? |

00:10:47 | Please think about... that okay? |

00:10:49 | Then how are you going to think about it? |

00:10:50 | Please show me how you are thinking about it. |

00:10:52 | That you can find it if you do such and such. |

00:10:57 | [ BB: Way of thinking ] |

00:10:59 | [ BB: Way of thinking ] |

00:11:00 | Okay. Go ahead. |

00:11:02 | Can you bargain and lower the price? |

00:11:04 | Ordinarily they wouldn't bargain, would they? |

00:11:07 | Although they might bargain if it |

00:11:08 | were at a vegetable or fish store. |

00:11:09 | I have never seen them bargain... at a cake store. |

00:11:13 | They might have bargained if it were Kenchan's Cakes, right? |

00:11:15 | Oh, don't you know it? |

00:11:16 | Ah, I did it. |

00:11:18 | Okay. Please think about it by yourself |

00:11:20 | for a while. About two minutes left. |

00:11:21 | I told you not to use this but to use the back, didn't I? |

00:11:23 | We're buying 10? |

00:11:24 | We're buying 10 anyhow. |

00:11:26 | You need to buy 10 so... please buy 10, okay? |

00:11:29 | Buy 10... |

00:11:30 | Because... what you really want is |

00:11:32 | to buy 10 230-yen cakes, right? |

00:11:36 | But if you buy 10 230-yen cakes how much will it cost? |

00:11:38 | Two thousand three hundred yen. |

00:11:39 | It'll end up being two thousand three hundred yen, right? |

00:11:41 | However, you only have 2,000- 2,100 yen in cash so... |

00:11:44 | You need to mix, mix it up or you can't buy it, you know? |

00:11:47 | Because you only have 210 yen in cash. |

00:11:49 | Then how do you need to think about it... |

00:11:52 | in order to find out how many 230-yen cakes to buy? |

00:11:55 | Please think about that. |

00:11:59 | Please think about it. |

00:12:00 | I don't care what kind of method you use. |

00:12:02 | Inequality equation. |

00:12:03 | Oh, if you want to set up an inequality equation |

00:12:05 | go ahead, that's fine, too. |

00:12:06 | If someone else says that they want to |

00:12:07 | think about it with a different method |

00:12:08 | because they don't need an inequality equation... |

00:12:10 | That, that is fine for that person, too. |

00:12:12 | I want to know how you think about it so... |

00:12:14 | I will ask you about thinking... |

00:12:16 | about how you thought about it. |

00:12:19 | See... being asked to figure out |

00:12:21 | how to think about it is more difficult |

00:12:23 | than being asked to solve an equation, isn't it? |

00:12:26 | Okay, go ahead. |

00:12:34 | Is it not permissible to buy nine? |

00:12:36 | I don't get this. |

00:12:59 | Don't get it? |

00:13:01 | But, if you really were buying two kinds of cake |

00:13:03 | you have to think about money, |

00:13:04 | the money that you have and the bill. |

00:13:06 | After you ask for the bill you can't say I'm sorry |

00:13:09 | I want to return this. Can you? |

00:13:11 | Then you exchange. |

00:13:14 | That has happened to me a lot, too. |

00:13:16 | I say oh, sorry! Please return this. |

00:13:26 | At any rate... please buy 10 cakes. |

00:13:28 | How are you going to think about it? |

00:13:38 | It's also okay if it's over 10, right? |

00:13:40 | Not over 10. Buy 10- |

00:13:42 | Buy 10? |

00:13:43 | Ten? |

00:13:44 | You're buying 10, you know. |

00:13:49 | Ten. |

00:13:50 | Ten. |

00:13:51 | It's not 11 or 12 or eight, but buy exactly 10, okay? |

00:13:57 | Well, then how can you... find out... how many you can buy? |

00:14:02 | There are people who...would have them take the cake, |

00:14:04 | take a 200-yen cake and break it in half |

00:14:06 | and make it 100-yen. |

00:14:07 | Okay, then you go to the cake store and |

00:14:09 | try and request that. |

00:14:10 | Most people won't do such a thing, you know. |

00:14:11 | It's different from asking to have |

00:14:13 | half a Japanese radish, you know. |

00:14:14 | If you ask them to halve the Japanese radish they'd do it for you. |

00:14:16 | It's okay... if it's a Japanese radish. |

00:14:19 | What if you said just the fresh strawberry |

00:14:21 | on the strawberry cake? |

00:14:22 | The fresh strawberries on the cakes are sour. |

00:14:29 | The strawberries on the cake need to be out |

00:14:31 | in the stores before they are fully ripe, |

00:14:34 | they are picked while they are sour, |

00:14:36 | so it can't get sweet. But this is unrelated... |

00:14:47 | So how do you think about this? |

00:14:53 | Not by using equations or things like that |

00:14:55 | but tell me what you have to do to get the answer. |

00:14:57 | Buying two thousand... two... 2,100 yen exactly... |

00:15:00 | We don't need to... it's okay if we have change left over, right? |

00:15:02 | It's okay if there's left over. |

00:15:03 | It's good if you have change in any case. |

00:15:05 | Change, or else it's also okay |

00:15:07 | if you use all of the 2,100 yen, you know. |

00:15:22 | Well there is one minute of remaining time. |

00:15:24 | I don't understand this. |

00:15:29 | You're all good at this setting up an equation |

00:15:31 | and suddenly spitting out an answer. |

00:15:33 | Try doing it with that method. |

00:15:55 | Okay. |

00:15:58 | Then... we'll have midway presentations. |

00:16:02 | Okay, please raise your heads. |

00:16:04 | Then people who think they have a way |

00:16:06 | that seems to work... |

00:16:08 | and understand the method |

00:16:09 | you are paper, right? |

00:16:11 | Not yet, now. |

00:16:12 | People who had no idea how to do it... |

00:16:14 | you're rock... okay? |

00:16:18 | Okay, people who think it's best to do it this way, but say... |

00:16:20 | You don't understand... you don't have confidence, are scissors, okay? |

00:16:26 | Although from looking at what you were writing |

00:16:27 | it seems like rocks are plentiful. |

00:16:28 | But, I'll try and ask you, okay? |

00:16:29 | Okay, then students who understood |

00:16:30 | the way of thinking are paper. |

00:16:33 | And then... people who say that you can do it |

00:16:35 | to some extent and you understand it are paper, okay? |

00:16:37 | People who say... I don't understand it at all are rock, okay? |

00:16:40 | People who say that they are in the middle are scissors, okay? Okay. |

00:16:42 | Then one, two, and... three. |

00:16:50 | Oh... there are no paper people. |

00:16:53 | What's paper? |

00:16:54 | Paper is people who say that they understand it completely. |

00:16:57 | One person. |

00:17:01 | Okay. |

00:17:02 | Then scissors people and paper people, |

00:17:05 | there are even quite a few rock people who responded, right? |

00:17:07 | Okay, then I will try and ask a few people, okay? |

00:17:09 | Okay, then Hara. |

00:17:11 | How did you think about it? |

00:17:13 | What? |

00:17:16 | Okay, go ahead. |

00:17:18 | I... didn't understand it at all but... |

00:17:25 | First of all... |

00:17:28 | I thought that I should calculate... |

00:17:34 | How many of the 230-yen ones I could buy and... |

00:17:38 | In the beginning... when I did it with 10... |

00:17:43 | It ended up being 2,300 yen so... |

00:17:47 | It's not good because it's over the amount so... |

00:17:50 | And then next when I did it with nine... |

00:17:55 | When I did it with nine... |

00:17:57 | it was 2,070 yen and... it was okay but, |

00:18:02 | you need to buy 10, so when I calculated it... |

00:18:07 | to buy one 200-yen cake... |

00:18:13 | Two... 2,070 plus... |

00:18:18 | Two hundred yen is... |

00:18:20 | With 2,270 yen and... |

00:18:23 | You go over. |

00:18:24 | You go over, don't you? Okay. |

00:18:25 | So then... you keep reducing the numbers and... |

00:18:28 | Keep reducing and... when you do it with eight on this side and two this side, then? |

00:18:29 | When I did it- |

00:18:30 | When you did it? |

00:18:32 | Time ran out and... |

00:18:33 | Time ran out and... |

00:18:34 | I couldn't do it to the end. |

00:18:35 | You couldn't do it to the end. |

00:18:37 | Okay. |

00:18:38 | Raise your hand... if you say that |

00:18:40 | this way of thinking was really similar to yours. |

00:18:43 | Hara started counting from 10, but... |

00:18:45 | there may be people who started counting from this side. |

00:18:48 | People who say that they used this way of thinking. |

00:18:52 | Okay. Only, Ikui? |

00:18:55 | Arai? |

00:18:56 | Okay. Then Ikui, Arai, Joji, right? |

00:18:58 | Then Ikui... where did you find |

00:19:02 | an answer that was exactly even? |

00:19:04 | Or could you not find the answer? |

00:19:06 | Were you at the point in which you were do- |

00:19:08 | counting it like this but time ran out? |

00:19:10 | Did you find it in a flash? |

00:19:14 | The 230-yen one... |

00:19:18 | You buy three of them and... |

00:19:19 | Three? Then how much does it become? |

00:19:22 | Six hundred ninety yen. |

00:19:23 | Six hundred ninety yen. |

00:19:24 | And what about this side? |

00:19:26 | Seven. |

00:19:27 | When you buy seven? |

00:19:28 | Two thousand ninety yen. |

00:19:29 | Wait a minute. |

00:19:30 | If you buy seven, if you buy seven |

00:19:31 | 200-yen ones how much does it become? |

00:19:33 | One thousand four hundred yen. |

00:19:34 | One thousand four hundred yen. Okay. |

00:19:35 | How much is it... if you add it? |

00:19:37 | Two thousand and seventy yen. |

00:19:38 | Two thousand- |

00:19:39 | Oh. Two thousand ninety yen. |

00:19:40 | Ninety yen. |

00:19:41 | Okay. That's what it's about. |

00:19:43 | So that means if you buy three 230-yen cakes |

00:19:46 | and seven 200-yen cakes, |

00:19:50 | then it becomes 2,090 yen. |

00:19:51 | You get 10 yen in change. |

00:19:53 | That's why you could buy three of these. |

00:19:55 | And as for this, if you buy seven then... |

00:19:57 | With 2,100 yen there is only 10 yen left. |

00:19:59 | And with only 10 yen you can't buy anything, so it's this. |

00:20:02 | You could find an answer... that it was this. |

00:20:07 | What about yours, Joji? |

00:20:08 | I'm not done yet. |

00:20:09 | Middle... You are still in the middle of doing it. |

00:20:11 | What about yours, Arai? |

00:20:15 | What? |

00:20:17 | I'm still doing it. |

00:20:18 | Still doing it. As for Arai, he couldn't |

00:20:21 | print out what was in the hard drive in his head, right? |

00:20:24 | Okay. That's what it's about. |

00:20:26 | This... then something else... |

00:20:28 | students who say, "I did this." |

00:20:32 | Kamon and Luiko and who else? |

00:20:35 | Other people. |

00:20:37 | No one? |

00:20:39 | What's yours, Kamon? |

00:20:41 | How do you... work it out? |

00:20:43 | What did you set up? |

00:20:47 | Huh? How did you do it? Your method? |

00:20:49 | Inequality equation. |

00:20:50 | You set up an inequality equation. Okay, what about Luiko's? |

00:20:51 | Inequality equation. |

00:20:52 | You set up an inequality equation? |

00:20:53 | Then what about other people? Isn't there anyone? |

00:20:58 | No one? |

00:21:01 | Then the other people can't buy them. |

00:21:02 | You know, the cakes, counting them one-by-one |

00:21:04 | is a really ordinary way of doing it, you know. |

00:21:05 | Isn't there anyone else? |

00:21:06 | Maruya's was also an inequality equation, right? |

00:21:09 | We'll get to you later, so wait a little, okay? |

00:21:10 | Other people. |

00:21:11 | How did you do yours, Bancho? |

00:21:13 | Huh? |

00:21:14 | Yeah. |

00:21:16 | You wrote multiply by something, |

00:21:17 | multiply by something, right? |

00:21:18 | How did you do that? |

00:21:19 | The same as that. |

00:21:20 | It's the same as this, right? |

00:21:21 | And then who else was it now? |

00:21:24 | Nagase's one also used a ratio, right? |

00:21:26 | Is it the same as this? |

00:21:27 | It's different? What is it? |

00:21:28 | Huh? |

00:21:29 | Inequality equation. |

00:21:30 | Inequality equation? |

00:21:31 | Okay. |

00:21:32 | Then... are there others? |

00:21:34 | Who used a completely different way of thinking? |

00:21:37 | No? |

00:21:38 | Then... I've thought about it, too, so... |

00:21:40 | what do you think about this way of thinking? |

00:21:42 | Do you all understand it? |

00:21:44 | You bought... ten... 230-yen cakes. |

00:21:50 | You're told to buy a lot and so in reality |

00:21:51 | you want to buy all 230 yen cakes, right? |

00:21:53 | Then how much money is needed? |

00:21:54 | [ BB: Method of thinking. Ten 230-yen cakes. ] |

00:21:55 | Two thousand three... |

00:21:56 | In reality 2,300 yen is required, right? |

00:22:00 | But you're short 200 yen. |

00:22:02 | You are short... 200 yen. |

00:22:06 | You're short. You thought... |

00:22:09 | that you would buy a cake that is... |

00:22:10 | 30 yen cheaper than... the 230-yen cake. |

00:22:11 | [ BB: Short 200 yen ] |

00:22:12 | Buy a cake that is 30 yen cheaper and... |

00:22:14 | You buy a cheap cake and... |

00:22:15 | replace this needed 200 yen for a cake |

00:22:16 | that is 30 yen cheaper, okay? |

00:22:17 | [ BB: 30-yen cake ] |

00:22:24 | You're short 200 yen, you know. |

00:22:25 | But, let's buy them a cake that's not 230 yen |

00:22:27 | but a cake... that is 30 yen cheaper. |

00:22:29 | Then 30 yen is going to be saved. |

00:22:31 | With each, 30 yen is going to be saved. |

00:22:33 | How many cakes that are 30 yen cheaper do you need |

00:22:35 | to buy in order to make up the 210 yen shortage? |

00:22:39 | This needed part. |

00:22:43 | How many cakes that are 30 yen cheaper do you need |

00:22:45 | to buy to make up the 210 yen shortage? |

00:22:47 | Can you make up the 210 yen? |

00:22:48 | Seven. |

00:22:50 | Yeah. If you buy six, six times three is 180 yen, |

00:22:53 | so you are still 20 yen in the red, right? |

00:22:56 | However... if you buy seven of these... |

00:22:57 | if you buy seven... |

00:22:58 | you will have 210 yen left over, right? The money, right? |

00:23:00 | [ BB: Seven ] |

00:23:03 | That 210 yen is applied to this 200 yen, you know. |

00:23:06 | Then if you buy seven of the cakes that are 30 yen cheaper, |

00:23:09 | if you do that, then what about this side? |

00:23:11 | Three. |

00:23:12 | It's three... did anyone do it like that? |

00:23:14 | Someone who did it like this? |

00:23:16 | There probably isn't anyone, right? |

00:23:17 | Start off by buying 10. |

00:23:19 | You're short 200 yen so... let's make up for the |

00:23:21 | missing cost with cake that is 30 yen cheaper. |

00:23:23 | You can make up for it if you buy seven, |

00:23:26 | so this is three. In that way. |

00:23:28 | It was good, right? Then I'll ask you. |

00:23:30 | Okay... Luiko. |

00:23:31 | Then how did you think... about this one? |

00:23:35 | The total 230 yen, oh... |

00:23:39 | It's for some amount and make that amount X and... |

00:23:46 | You need to buy 10 of the 200-yen ones. |

00:23:50 | So 10... make it 10 minus X and... |

00:23:55 | And the total has some amount of two- 230-yen ones. |

00:24:02 | And the 230-yen ones are 230 X. And... |

00:24:07 | the 200-yen one is 200... |

00:24:11 | bracket 10 minus X... And then... then... |

00:24:19 | 200- 230 X plus 200 bracket 10 minus X... |

00:24:28 | is less than, minus, less than or equal to 2,100 yen. |

00:24:36 | And you form the inequality equation. |

00:24:39 | Okay. |

00:24:40 | You said that this was the inequality equation, right? |

00:24:43 | Okay. |

00:24:44 | Did you understand the meaning? |

00:24:46 | Perfect. |

00:24:47 | You get it better with Luiko's explanation than with mine. |

00:24:49 | Okay. Try and raise your hands. |

00:24:50 | People who say that they got it with Luiko's explanation. |

00:24:53 | One person? |

00:24:54 | Only Maruya? Two people? Three people? |

00:24:56 | Four people? Just four people is it? Five people? Okay. |

00:25:00 | Then... please explain it next, Ryo. |

00:25:01 | Please explain it in a way that is a little more understandable. |

00:25:03 | Try and explain it in a way in which... |

00:25:06 | a few more people will say... that they understood. |

00:25:09 | The method of explanation is okay with this. |

00:25:13 | Okay. |

00:25:15 | Go ahead. |

00:25:19 | Okay. Go ahead. |

00:25:25 | You can't do it? |

00:25:26 | You don't know? |

00:25:32 | Okay. Then... I'll start talking from this point okay? |

00:25:36 | To tell you the truth I was going to |

00:25:38 | talk about today, what Luiko set up. |

00:25:41 | But I wanted you to find a number... |

00:25:42 | of ways to come up with it so... |

00:25:44 | I did it so that I would have you think about it, right? |

00:25:47 | Three, four, five, six. Okay. |

00:25:48 | One, two, three, four, five, six. |

00:25:50 | Okay. |

00:25:52 | One, two, three, four, five, six. |

00:25:54 | Oh, it's not five, six... |

00:25:56 | there's five people here. |

00:25:58 | One, two, three, four, five, six. Here. |

00:26:22 | Okay. From there, and so... |

00:26:26 | While talking so that everyone will say, |

00:26:28 | "I see," while understanding Luiko's explanation, |

00:26:31 | we are going to try and do it using that problem, |

00:26:33 | using an inequality equation problem, okay? |

00:26:35 | You want to buy a total of 10 cakes in which |

00:26:37 | one is 200-yen and the other is 230 yen. |

00:26:41 | And you want to make the total less than 2,100 yen. |

00:26:44 | In order to buy as many 230-yen cakes as possible, |

00:26:47 | what is the maximum that you can buy? |

00:26:49 | That is the problem. |

00:26:50 | And what is the thing that you want to find? Pinko? |

00:26:53 | What do you need to answer? |

00:26:55 | How many 230 yen cakes you buy. |

00:26:58 | It's a problem asking how many 230 yen cakes |

00:27:00 | you can buy, so... |

00:27:02 | So that's why you're going to think of it |

00:27:04 | as changing the 230-yen cake into X. |

00:27:06 | I'm asking how many can you buy, |

00:27:07 | so you should think of changing the 230-yen cake into X. |

00:27:09 | [ BB: Buy X amount of 230-yen cakes ] |

00:27:14 | When doing that... you need to buy |

00:27:17 | 10 cakes all together. You need to buy ten. |

00:27:21 | Right? |

00:27:22 | Then, Qumi? If it's six of this cake, then... |

00:27:26 | how many of this cake do you need to buy? |

00:27:29 | Four. |

00:27:30 | Four. How did you calculate it? |

00:27:32 | What? |

00:27:34 | Four. |

00:27:35 | So how do you calculate it? |

00:27:36 | How do you know that this is four? |

00:27:39 | What? |

00:27:40 | Because it's not enough. |

00:27:42 | Yeah, so how do you calculate it? |

00:27:44 | What's the equation here? |

00:27:46 | Add. |

00:27:47 | Huh? |

00:27:48 | What do you add to six to get this ten? |

00:27:50 | Then... then how many is it here? |

00:28:07 | X. |

00:28:08 | What? |

00:28:09 | That's why you're in trouble |

00:28:10 | if you are fooled by the number here. |

00:28:12 | If this is six then it's probably how many here, Ryusaki? |

00:28:16 | Qumi is saying that it's four, |

00:28:18 | but how do you get this here? |

00:28:21 | It's four, but how do you come up with four? |

00:28:27 | Ryusaki, how do you come up with four here? |

00:28:29 | Subtract. |

00:28:30 | You need to subtract, right? |

00:28:31 | It's good if 10 minus six is four here. |

00:28:33 | If it was seven here, then you would |

00:28:36 | write 10 minus seven, right? |

00:28:38 | If this were nine here then you would |

00:28:40 | think of this as 10 minus nine. |

00:28:43 | So if you subtract one of the numbers |

00:28:44 | from this number, from the total number, |

00:28:46 | then you get the remaining number. |

00:28:48 | And the problem is, |

00:28:50 | if you make the number on this side X, |

00:28:52 | then what will this be if you do that? |

00:28:54 | Here. |

00:28:57 | Joji. What will this become? |

00:29:01 | Here. |

00:29:03 | You haven't been listening, have you. |

00:29:05 | If this were three, |

00:29:06 | then this can be found by going 10 minus three. |

00:29:08 | If this were four, then this is 10 minus four. |

00:29:11 | If this is five, then this is 10 minus five. |

00:29:13 | Then if this is X, then what is this? |

00:29:16 | Ten minus X. |

00:29:17 | Yeah. It'll become ten minus X. |

00:29:20 | What this is saying is that you can only buy |

00:29:22 | 10 minus X number of the 200-yen cakes. |

00:29:25 | It will come up here. |

00:29:26 | It's 10 altogether and if you make this X, |

00:29:29 | then here... you need to subtract this number. |

00:29:31 | If you subtract this number from 10 |

00:29:32 | then you'll always arrive at the number left over. |

00:29:34 | That's why it'll be the case that |

00:29:36 | you can buy this many 200-yen cakes. |

00:29:38 | The amount you bought, right? |

00:29:40 | This will be the amount here. |

00:29:41 | If you do that, what would the cost be |

00:29:43 | if you bought only X number of 230-yen cakes? |

00:29:48 | If you multiply the 230-yen cakes at this price |

00:29:50 | by X then you'll get the total cost, right? |

00:29:52 | It's 230 X, you know. |

00:29:53 | Because you're only going to buy 10 minus X |

00:29:55 | of the 200-yen cakes, the cost will be this. |

00:29:58 | Then since you only have 2,100 yen with you, |

00:30:00 | you'll be in trouble... |

00:30:01 | if it isn't less than this. |

00:30:03 | And so you will get this equation, okay? |

00:30:07 | What is the equation? |

00:30:08 | Oh, I can't write it, can I? |

00:30:10 | I'm wondering what the equation is so... |

00:30:11 | The equation is 230 X plus |

00:30:13 | 200 bracket 10 minus X is less than or equal to... |

00:30:15 | [ BB: Equation ] |

00:30:18 | Two thousand one hundred. |

00:30:22 | Okay, then let's try and solve this, okay? |

00:30:24 | Okay, the 230 of this 230 X stays the same. |

00:30:27 | Okay, Sakai, |

00:30:28 | how much is it here when you take the parentheses off? |

00:30:30 | Huh? |

00:30:31 | I took the brackets off now, so here. |

00:30:35 | Multiply this and this. |

00:30:37 | Mm? |

00:30:38 | How much is it when you multiply it? |

00:30:49 | How much is it if you take off the brackets? |

00:30:56 | Well then how do you do two bracket X plus three? |

00:31:00 | Two X. |

00:31:02 | Well then remove the brackets. |

00:31:11 | I did it. I did it. |

00:31:20 | Four plus five. |

00:31:25 | You multiply it, right? |

00:31:34 | Huh? |

00:31:35 | Bracket... 200 times 10 is see... |

00:31:41 | Two thousand. |

00:31:42 | Oh, 2,000, right? Two thousand. Okay. |

00:31:44 | Two thousand... minus, you multiply this so... |

00:31:46 | this time on this side so okay. |

00:31:47 | Two hundred X. |

00:31:48 | Two, 200 X. Okay. Less than or equal to 2,100. |

00:31:53 | Okay. Then which is the next one that you transpose? |

00:31:55 | Two thousand. |

00:31:56 | Two thousand. Okay. |

00:31:57 | We're going to bring the plus 2,000 to the other side. |

00:31:59 | And 230 X minus 200 X is |

00:32:03 | less than or equal to 2,100 minus 2,000. |

00:32:08 | The sign changes, so please be careful, okay? |

00:32:09 | When you transpose it, okay? |

00:32:10 | Then 30 X... 30 X is less than or equal to... |

00:32:13 | 100. Okay. |

00:32:17 | Then you're going to divide both by 30 on both sides, |

00:32:20 | so it becomes X is less than equal to... |

00:32:23 | 100... thirtieths but... |

00:32:26 | I'll erase the zero here, okay? It'll become 10- |

00:32:29 | Thirds. |

00:32:30 | Thirds. |

00:32:31 | What will 10 become if you write it in decimals? |

00:32:36 | Three point three three three three three, right? |

00:32:39 | If I asked you to find the largest integer... |

00:32:42 | that is smaller than three point three... |

00:32:45 | it will come out as three. |

00:32:47 | I can't really write the answer, but okay... |

00:32:48 | you can buy three... up to three... of the 230-yen... |

00:32:51 | thirty yen... cakes. |

00:33:00 | If you present it... like this... it's good. |

00:33:04 | Things presented like this are |

00:33:05 | solved using an inequality equation. |

00:33:07 | [ BB: You can buy up to three of the 230-yen cakes. ] |

00:33:09 | Which is easier, doing it one-by-one or |

00:33:11 | using an inequality equation? |

00:33:13 | An inequality equation. |

00:33:14 | It's easier to use the inequality equation, isn't it? |

00:33:16 | And so today what I would like you to do from here is, |

00:33:19 | we already did this in the method of thinking but... |

00:33:21 | Inequality equation. |

00:33:23 | I would like you... to know... |

00:33:26 | the good qualities of... |

00:33:38 | finding the answer by... |

00:33:41 | setting up an... inequality equation, |

00:33:43 | right... inequality equation so... |

00:33:45 | we thought about it... with a problem like this. |

00:33:47 | [ BB: Learning the good qualities of finding the answer by setting up an inequality equation. ] |

00:33:50 | If you were to solve it without using an inequality equation |

00:33:52 | you need to check it out quite a lot, one-by-one, a lot. |

00:33:55 | Hara could solve it because it was 10, |

00:33:58 | but what if you were to buy |

00:34:00 | 100 of these two cakes together... |

00:34:04 | Ninety- figure out 100, |

00:34:06 | and figure out 99, and figure out 98, |

00:34:08 | and figure out 97, and- |

00:34:10 | You need to figure out all of the numbers |

00:34:12 | between one and 100, don't you? |

00:34:14 | However, if you used a method like this that Luiko used... |

00:34:18 | you will arrive at the answer quickly. |

00:34:20 | Therefore, you don't need to figure out each number one-by-one. |

00:34:22 | So working it out by making... |

00:34:25 | an inequality equation has a lot more... |

00:34:28 | good qualities... than counting it one-by-one. |

00:34:30 | That's what it's about, all right? |

00:34:32 | So then and so... |

00:34:33 | if there are good qualities like that then... |

00:34:36 | we're saying that. |

00:34:38 | So there are two problems on the right side. |

00:34:41 | This time, please buy 20 apples and oranges altogether. |

00:34:43 | If you count it one-by-one |

00:34:45 | you will be in an incredibly terrible situation. |

00:34:47 | As we just did in the cake situation, |

00:34:50 | set up an inequality equation by yourself and |

00:34:52 | find out up to how many apples you can buy. |

00:34:54 | Or if you're doing the problem at the bottom, |

00:34:56 | try to solve the problem about |

00:34:57 | how many pears you can buy by setting up an inequality equation. |

00:34:59 | Work it out and find an answer. |

00:35:02 | Because finding the answers one-by-one is hard- |

00:35:04 | I wonder if you see the numerous good points |

00:35:05 | of setting up inequality equations, |

00:35:07 | and, well, that you'll set up |

00:35:09 | inequality equations yourself and |

00:35:11 | try to find the solutions. |

00:35:13 | That's what it's all about, okay? |

00:35:14 | Is it okay? |

00:35:16 | Okay. Then and so... |

00:35:18 | people who haven't written this here, |

00:35:20 | write it, and then do problem one. |

00:35:23 | Try to set up an inequality equation |

00:35:25 | by yourself in the same way and |

00:35:27 | try to solve the problem. |

00:35:30 | Okay. Go ahead. |

00:35:41 | This is... the total so... |

00:35:43 | you don't have it... see? |

00:35:47 | This is attached. |

00:36:01 | It's faster than counting, right? |

00:36:12 | It's okay. Now, work out the problem. |

00:36:14 | This expresses this in the same way as this. |

00:36:17 | Oh, solve this on the top. |

00:36:28 | That's good. |

00:37:14 | It's like this, you know. |

00:37:16 | Twelve times. |

00:37:18 | Not 12, it's 70 times 20, you know. |

00:37:21 | This is 20, isn't it? |

00:37:23 | It's a bracket so, okay? |

00:37:24 | It's not a 12, you know. |

00:37:26 | I got it. Twenty. |

00:37:28 | You couldn't read the |

00:37:30 | numbers that you wrote, could you? |

00:37:47 | It's okay, Tanizaki, here. |

00:37:50 | Try this and work it out like this. |

00:37:58 | Sakai's one is also good, isn't it? |

00:38:00 | Okay, you've got it. |

00:38:06 | Then now it's easy, right? |

00:38:08 | It's easy, right? |

00:38:11 | This isn't X here, but... |

00:38:13 | you're going to buy 20 in all, right? |

00:38:16 | So here you will get the number you subtracted... |

00:38:18 | from the total amount of 20. |

00:38:24 | And so 20 minus... negative X. |

00:38:29 | And so the price here... |

00:38:31 | you multiply the price of one of them, and |

00:38:34 | this amount, so this becomes 120 X. Okay? |

00:38:39 | And what about this one? |

00:38:41 | It becomes 70 parentheses. |

00:38:45 | You can't write it... if it's like that. |

00:38:46 | Please write the 70 sort of more on the side. |

00:38:50 | And what about here? |

00:38:53 | Twenty minus X. |

00:38:55 | Okay. Now you've got it. |

00:38:56 | And then put these together and |

00:38:58 | make this smaller than four. |

00:38:59 | What about you, Uchida? |

00:39:00 | Huh? Two hundred. |

00:39:06 | Just a moment. It's all right now, right? |

00:39:11 | Oh, Ueda, that's good. Okay, it's done. |

00:39:16 | Oh, Ueda, yours is good, too. |

00:39:17 | You've arrived at the answer, right? Okay. |

00:39:18 | Where'd it go, Waka? |

00:39:24 | This is okay, you know? |

00:39:27 | This is... 120 X plus, |

00:39:30 | how much is this if you multiply it by this? |

00:39:33 | Two times seven, 14, right? |

00:39:36 | One thousand four hundred seventy two thousand. |

00:39:42 | This is four. Then you have to transpose it. |

00:39:44 | There is seven, 700. |

00:39:46 | Twent- this is 70 times 20, so next is four, right? |

00:39:52 | Okay. |

00:40:46 | [ BB: 120-yen apples ] |

00:40:55 | [ BB: 70-yen tangerines ] |

00:40:56 | [ BB: Total ] |

00:41:57 | Okay, I guess I'll have you write it. |

00:42:07 | Are you done? |

00:42:08 | [ BB: Buying Fifteen. Seventy-yen pears. Fifty-yen persimmons. Basket. Total. ] |

00:42:09 | Did you do it? |

00:42:10 | Then work it out there... will you? |

00:42:14 | This should be fine, right? |

00:42:17 | [ BB: Buying Twenty. One hundred twenty-yen apples. Seventy-yen tangerines. Total. ] |

00:42:18 | Could you write it? |

00:42:20 | Isn't it good? It's good. |

00:42:22 | Divide, you can divide it. |

00:42:29 | Then... Bancho. |

00:42:30 | Please write number two, okay? |

00:42:31 | Look at the figure and set up an equation |

00:42:33 | and work it out, okay? |

00:42:34 | What number? |

00:42:35 | Number two. |

00:42:37 | Number two? |

00:42:38 | Yeah. |

00:42:50 | Write it without looking at anything, okay? |

00:42:52 | Because I wrote-wrote that you would buy 15. |

00:43:02 | Mm, I just saw someone's eyes. |

00:43:03 | Okay, Watabe. |

00:43:04 | Uh, wait a second. |

00:43:05 | Watabe, please write number one, okay? |

00:43:07 | Okay, go ahead. |

00:43:09 | You don't understand if you don't look at anything. |

00:43:10 | It's not written. |

00:43:12 | This is going to appear in the equation. |

00:43:14 | Oh, how much is it for the baskets? |

00:43:15 | Oh yeah, I didn't write the basket prices. Sorry. |

00:43:17 | The basket price is... |

00:43:19 | Eighty yen, isn't it? |

00:43:20 | Eighty yen. |

00:43:38 | The total... was 1,000 yen, wasn't it? |

00:43:40 | Hm? Oh. I should write the totals, too, shouldn't I? The total, sorry. |

00:43:43 | Less than 1,000 yen. |

00:43:45 | Watabe's is less than 2,000 yen. |

00:43:46 | Two thousand? |

00:43:48 | Please write 2,000 yen here. Oh, okay. |

00:43:56 | Try hard and work it out. |

00:44:03 | Just one more step, just the answer. |

00:44:05 | Oh, you need to display the answer. |

00:44:11 | Eight? |

00:44:14 | It's wrong? |

00:44:15 | What? |

00:44:16 | What is this? |

00:44:17 | What? |

00:44:18 | It's wrong. This, the answer |

00:44:19 | of this inequality equation is wrong, isn't it? |

00:44:21 | Isn't it okay? Because... this is 10, right? |

00:44:26 | Is this... the answer? |

00:44:30 | With 80? |

00:44:32 | It's this value here. |

00:44:33 | Two times nine? |

00:44:34 | What about eight? |

00:44:35 | Seven hundred fifty. |

00:44:37 | Aren't you missing the 50 here? |

00:44:45 | Oh... the response is okay with this. |

00:44:48 | The answer is not this though, is it? |

00:44:54 | Huh? |

00:44:55 | The answer is- |

00:44:56 | What is the answer? |

00:44:57 | Is it this? |

00:44:58 | This is good. |

00:45:00 | This is the answer to the inequality equation. |

00:45:02 | But, the answer to the problem has to be this, right? |

00:45:10 | When asked to work out this inequality problem, |

00:45:12 | this is- This has to be the answer here, right? |

00:45:14 | However, this won't be the answer to the applied problem so- |

00:45:16 | One hundred seventy over 20. |

00:45:19 | Seventeen over two, right? |

00:45:22 | So teacher, if you do it like this, is it correct? |

00:45:33 | That should be that way, right? Okay. |

00:45:38 | Ueda, how far did you go? |

00:45:44 | Fifty times 15 is look... |

00:45:46 | Not yet? |

00:45:49 | It's 75, you know. Then it becomes 750. |

00:45:54 | For example, how do we write the answer? |

00:45:56 | What are you going to write? |

00:45:57 | The problem asks up to how many can you buy. |

00:46:00 | What? Pears, right? |

00:46:02 | Up to how many pears can you buy? |

00:46:09 | It's 70 times 20, so it's not 140, |

00:46:12 | but it's only one zero, right? |

00:46:18 | Who can read this? |

00:46:19 | Who can't read this? |

00:46:41 | There the six is... 60... you're missing one zero, aren't you? |

00:47:12 | Okay... that's what it's about. |

00:47:14 | Please look at number one first. If you say that you will buy only X 120-yen apples then... |

00:47:20 | You're going to buy a total of 20. |

00:47:22 | So, as for the tangerines, you need to buy only the total 20 minus X tangerines. |

00:47:26 | And the price of the apples is 120 X. |

00:47:29 | And the price of the tangerines is 70 parentheses 20 minus X. |

00:47:32 | And the total that you have is 2,000 yen, you know. |

00:47:35 | So you're asked to make it less than 2,000 yen so... |

00:47:37 | One hundred twenty X plus 70, parentheses 20, minus X, is less than or equal to 2,000. |

00:47:42 | And if you try to find the answer you get X is less than or equal to 12. |

00:47:47 | That's why you can buy up to 12 apples. |

00:47:50 | We're going to try to see if this is true or not, okay? |

00:47:54 | You buy 12 120-yen apples. |

00:47:58 | Then what is the cost? |

00:48:01 | Is there anyone who knows what is 12 times 12? |

00:48:03 | Didn't I teach this to you before? |

00:48:04 | One hundred forty four. |

00:48:05 | It's 144, right? Okay. One thousand four hundred forty yen. This is the price of the apples. |

00:48:09 | Then, you need to buy eight of the 70-yen tangerines so seven times eight, 56. |

00:48:14 | And all together it's exactly 2,000 yen. |

00:48:20 | About it being exactly 2,000 yen, why did it become exactly 2,000 yen here? |

00:48:23 | Since it's divisible. |

00:48:24 | Because here we got 12, a number that was divisible, right? |

00:48:26 | Right. We got it because the 12 could be divided perfectly into it here, right? |

00:48:28 | That's why it ended up being exactly 2,000 yen. |

00:48:30 | However, this side. Okay. |

00:48:32 | You find it in the same way. The pears are X and you're going to buy 15, so the persimmons are 15 minus X. |

00:48:37 | The price of the pears and the price of the persimmons... and even the basket will be included as well this time, right? |

00:48:42 | It's asking you to limit it to 1,000 yen all together. So, if you set up an inequality equation you get this kind of equation. |

00:48:46 | Seventy X plus 50, parentheses 15, minus X, plus 80, is less than or equal to 1,000. Please work this out. |

00:48:56 | This is the answer of the inequality equation, okay? |

00:48:59 | You need to present this, okay? |

00:49:00 | Instead of just suddenly writing the answer eight- if you first work this out... |

00:49:04 | You get an answer of 17 halves, okay? |

00:49:07 | You need to find this first. Now you need to pinpoint it like this. |

00:49:14 | Then... if you buy eight 70-yen pears, then seven times eight equals 560 yen. |

00:49:19 | If you do that, then how many 50-yen persimmons do you buy? |

00:49:23 | You buy seven? Then seven times five equals 350 yen. All together... 910 yen. |

00:49:32 | Then... you'll have 90 yen in change coming back. |

00:49:34 | What? |

00:49:35 | The basket price. |

00:49:36 | Oh, there's the price of the basket. |

00:49:37 | The basket price is 80 yen so... |

00:49:40 | It's altogether 990 yen, and you'll only get 10 yen in change. That's what it's about. |

00:49:45 | What we talked about today was... the answer from inequality equations... that is... |

00:49:50 | When solving problems it's often easier to set up an inequality equation and find the answer, |

00:49:54 | than count things one-by-one and find the number. |

00:50:01 | That's why although it may be tedious... for the applied problems of inequality equations, okay? |

00:50:05 | Instead of looking for the answer one-by-one you find it by changing the parts written in Japanese to mathematical terms and solving it. |

00:50:15 | Because an inequality equation has a good quality like this. This is what we talked about. |

00:50:20 | Is it okay? |

00:50:22 | Is it okay? |

00:50:23 | Yes, okay. |

00:50:25 | Then I'll pass out the problems and finish off. What number should I pass out, today? |

00:50:29 | Is it number nine? |

00:50:32 | It's number nine. Number 10. |

00:50:33 | Then I'll hand out the problems for number 10 and finish. |

00:50:36 | From what number to what number are there? |

00:50:38 | It ends with 10. |

00:50:39 | Inequality equations end with this. |

00:50:46 | One, two, okay. |

00:50:54 | Four more. |

00:50:55 | Four more? Okay. |

00:50:56 | One, two, three, four, okay. |

00:50:59 | One, two, three, four, five, okay. |

00:51:02 | One, two, three, four, five, six, okay. |

00:51:07 | Okay. |

00:51:09 | Okay. Then we'll say our greetings and finish off. |

00:51:12 | Student officer. Lead with strong voices since we're finished. |

00:51:18 | Please get ready to bow. |

00:51:19 | Stand. |

00:51:33 | Thank you very much. |

00:51:34 | Thank you very much. |