Backsolving.
成绩单
词问题策略。所以，到目前为止整个问题模块我们已经谈过了这一点
直接的代数解决问题，始终是那些工作，这总是一种解决问题的方法，但这不是唯一的方法。
在这套视频中，我们将谈论您可以使用的一些替代策略。
The first strategy we're gonna talk about is backsolving. If all five answer choices are numerical, 如果我们得到五个数字，那么我们可以使用称为BackSolving的策略。BackSolving意味着我们首先假设其中一个数字答案是 答案的答案，我们选择一个，我们说，好的，让假装这是答案。
从这一点，我们向后工作，看看它是否真的是有意义的。如果答案不起作用，我们经常可以告诉我们需要更大或更大 smaller number for the end result, and this allows us to eliminate more than one answer at a time. A relatively simple way to approach this is always begin with answer choice C. So this is the most straightforward backsolving strategy.
If you start with C, that will be correct 20% of the time, and if it's not correct, you will be able to eliminate either the two larger answers or 两个较小的答案。所以就在一个试验中，即使你没有得到正确的答案， you can usually eliminate three answers at once, and then all you have to do is test one, of the remaining two.
There's alternative strategy, so this is a little more sophisticated, but you can certainly use this if you like. Alternate strategy would be to pick B first. There's a 20% chance that it's the official answer, and 另外20％的几率太大，这将使官方答案成为一个官方答案，让你在第一次猜测中获得了40％的机会。
当然，如果B不起作用，那么您将使用D next，然后将所有内容缩小到单个答案。 So that's a slightly more sophisticated approach but statistically it gets you to the right answer on average a little bit faster. So certainly it's something to consider. Okay, here's a practice question, pause the video, and then we'll talk about this.
Okay, this is a relatively easy practice question. In a certain state, schools pay 2% tax on food and 8% tax on stationery. The school placed a combined order of $500 on food and stationery and paid $19 on tax on the order. 这笔钱花了多少钱？所以，我们可以解决这个问题，我们可以设置代数并解决这个问题。
Instead of doing that, we're gonna explore a backsolving approach. So we're just gonna pick C, we're just gonna say pretend 300 is the answer, 这意味着他们在食物上花了300，所以他们必须在文具上度过200。对食物有2％的税，所以300的2％给予了6美元， 对文具有8％的税，所以给予16美元，总税22美元，这太多了。
They paid $19 in tax, so 22 is too much and so what this means is, to pay less in taxes the school must have spent more on food and less on stationery. Cuz food is taxed on a much lower rate, so if they spent more on food, they would be paying less in taxes. So right away we can eliminate A, B, and C, so this is great. Even if we were running out of time, we could guess from the remaining two and 我们会有一个very high likelihood of, of guessing by chance the right answer because 3 answers have already been eliminated.
But that was pretty quick, so we probably would have time still to do another round of backsolving. 所以另一轮，我们可以选择D或E.我只是选择了它，因为它已被100划分， 这只是稍微更方便，所以这是我要选择它的唯一原因。让我们说e是答案。
Well that means that food costs $400 if stationery costs $100, the food tax 2% of 400 is $8, 8% of 100 of course is $8 and 这将给我们一个总体的16美元的税收too little. So A, B, and C are too big, E is too little as far as the amount of tax and 所以这留下了唯一正确的答案。唯一可能的答案是D。
So after two choices, we are done, we know that D has to be the answer. Here's another practice question, pause the video, and then we'll talk about this. Okay. This is a mixture problem. If you haven't seen the video on, on mixture questions, it may help to go back and watch that video before talking about this particular problem because this particular problem depends on knowledge of that video.
A chemical supply company has 60 liters of 40% of some chemical, that chemical happens to be nitric acid. 你不需要担心。化学家必须增加多少升纯净的纯酸 所得溶液是50％的溶液？所以，我们会增加溶质以增加浓度和 we want to increase it to 50%.
所以，C是一个很好的圆形数字，所以我们只需选择C作为我们的答案。在甚至选择之前，请注意的是 在开始解决方案中溶质，40％的60％是24升。初始溶液中有24升酸。 所以，现在让我们选择更多升酸，因为这意味着我们具有总浓度 of 44 liters, that is the amount of acid in the solution and of course, the total solution, the volume of the solution is gonna be 80 liters and so we wanna know do we have the right concentration.
好吧，我们不必做分部。我们可以看到44多人超过80。 So we don't even note, need to know the exactly number. All we need to know is the concentration would be over 50%, so this is too high. We've added too much acid. So right away, we can eliminate C, D, and E.
所有这些都会添加过多的酸。所以现在我们必须挑选一个或b，没关系。 I'll just pick A. Suppose we add 12 liters of acid. 现在现在总浓缩物是24加12,36升酸。所以这是解决方案中有多少升酸总量， at that point of volume, the total volume of the solution would be 72, and notice that 36 is exactly half of 72 so this would be a 50% solution, this answer actually works, so we picked the right answer here, the answer is A.
In summary, when all five answer choices are numbers, one alternative strategy is to solve by backsolving. So the very straightforward approach is, start with answer C, try this as the answer to the prompt to see if it works in the scenario. If C doesn't work, the information about too big or too small. Will allow us to eliminate other answers, and 记住替代策略是选择，例如，你可以，你可以确定B或A是答案，具体取决于 它是否正确或太大，或者太小，如果它不起作用。
然后你可以选择d，第二选择会让你缩小一切。
阅读完整成绩单
The first strategy we're gonna talk about is backsolving. If all five answer choices are numerical, 如果我们得到五个数字，那么我们可以使用称为BackSolving的策略。BackSolving意味着我们首先假设其中一个数字答案是 答案的答案，我们选择一个，我们说，好的，让假装这是答案。
从这一点，我们向后工作，看看它是否真的是有意义的。如果答案不起作用，我们经常可以告诉我们需要更大或更大 smaller number for the end result, and this allows us to eliminate more than one answer at a time. A relatively simple way to approach this is always begin with answer choice C. So this is the most straightforward backsolving strategy.
If you start with C, that will be correct 20% of the time, and if it's not correct, you will be able to eliminate either the two larger answers or 两个较小的答案。所以就在一个试验中，即使你没有得到正确的答案， you can usually eliminate three answers at once, and then all you have to do is test one, of the remaining two.
There's alternative strategy, so this is a little more sophisticated, but you can certainly use this if you like. Alternate strategy would be to pick B first. There's a 20% chance that it's the official answer, and 另外20％的几率太大，这将使官方答案成为一个官方答案，让你在第一次猜测中获得了40％的机会。
当然，如果B不起作用，那么您将使用D next，然后将所有内容缩小到单个答案。 So that's a slightly more sophisticated approach but statistically it gets you to the right answer on average a little bit faster. So certainly it's something to consider. Okay, here's a practice question, pause the video, and then we'll talk about this.
Okay, this is a relatively easy practice question. In a certain state, schools pay 2% tax on food and 8% tax on stationery. The school placed a combined order of $500 on food and stationery and paid $19 on tax on the order. 这笔钱花了多少钱？所以，我们可以解决这个问题，我们可以设置代数并解决这个问题。
Instead of doing that, we're gonna explore a backsolving approach. So we're just gonna pick C, we're just gonna say pretend 300 is the answer, 这意味着他们在食物上花了300，所以他们必须在文具上度过200。对食物有2％的税，所以300的2％给予了6美元， 对文具有8％的税，所以给予16美元，总税22美元，这太多了。
They paid $19 in tax, so 22 is too much and so what this means is, to pay less in taxes the school must have spent more on food and less on stationery. Cuz food is taxed on a much lower rate, so if they spent more on food, they would be paying less in taxes. So right away we can eliminate A, B, and C, so this is great. Even if we were running out of time, we could guess from the remaining two and 我们会有一个very high likelihood of, of guessing by chance the right answer because 3 answers have already been eliminated.
But that was pretty quick, so we probably would have time still to do another round of backsolving. 所以另一轮，我们可以选择D或E.我只是选择了它，因为它已被100划分， 这只是稍微更方便，所以这是我要选择它的唯一原因。让我们说e是答案。
Well that means that food costs $400 if stationery costs $100, the food tax 2% of 400 is $8, 8% of 100 of course is $8 and 这将给我们一个总体的16美元的税收too little. So A, B, and C are too big, E is too little as far as the amount of tax and 所以这留下了唯一正确的答案。唯一可能的答案是D。
So after two choices, we are done, we know that D has to be the answer. Here's another practice question, pause the video, and then we'll talk about this. Okay. This is a mixture problem. If you haven't seen the video on, on mixture questions, it may help to go back and watch that video before talking about this particular problem because this particular problem depends on knowledge of that video.
A chemical supply company has 60 liters of 40% of some chemical, that chemical happens to be nitric acid. 你不需要担心。化学家必须增加多少升纯净的纯酸 所得溶液是50％的溶液？所以，我们会增加溶质以增加浓度和 we want to increase it to 50%.
所以，C是一个很好的圆形数字，所以我们只需选择C作为我们的答案。在甚至选择之前，请注意的是 在开始解决方案中溶质，40％的60％是24升。初始溶液中有24升酸。 所以，现在让我们选择更多升酸，因为这意味着我们具有总浓度 of 44 liters, that is the amount of acid in the solution and of course, the total solution, the volume of the solution is gonna be 80 liters and so we wanna know do we have the right concentration.
好吧，我们不必做分部。我们可以看到44多人超过80。 So we don't even note, need to know the exactly number. All we need to know is the concentration would be over 50%, so this is too high. We've added too much acid. So right away, we can eliminate C, D, and E.
所有这些都会添加过多的酸。所以现在我们必须挑选一个或b，没关系。 I'll just pick A. Suppose we add 12 liters of acid. 现在现在总浓缩物是24加12,36升酸。所以这是解决方案中有多少升酸总量， at that point of volume, the total volume of the solution would be 72, and notice that 36 is exactly half of 72 so this would be a 50% solution, this answer actually works, so we picked the right answer here, the answer is A.
In summary, when all five answer choices are numbers, one alternative strategy is to solve by backsolving. So the very straightforward approach is, start with answer C, try this as the answer to the prompt to see if it works in the scenario. If C doesn't work, the information about too big or too small. Will allow us to eliminate other answers, and 记住替代策略是选择，例如，你可以，你可以确定B或A是答案，具体取决于 它是否正确或太大，或者太小，如果它不起作用。
然后你可以选择d，第二选择会让你缩小一切。
