所以在本模块的第一组视频中，我们将重点讨论解决单词问题的代数方法。 I want to frame this by saying don't get locked into the mindset that algebra is the only way to do word problems. This is not the only way, in fact for some word problems it might not be the best way to do the word problem.

We're covering algebra first because it's the most widely applicable. It applies to the widest variety, the largest number of word problems. So, that's why we're beginning it first. Just have in the back of your mind that algebra is not the only way to do this. Okay, having said that, we're going to do algebra first. And, of course if we're going to do Algebra, we need variables.

To solve a word problem algebraically, we need to introduce variables. The very first thing I will say is, be thoughtful in the choice of your letter for the variable. It's true that, in algebra, the math we do does not depend on the letter at all. It's the same math. It doesn't matter what letter we pick for the variable.

尽管如此，你还是可以选择一封有意义的信。例如，选择一个以 the same letter of the name of the person or the thing for which it stands. Don't pick plain old x. See everyone, when they start doing algebra, they think it's a law they have to use x for algebra.

And x is not necessarily the best choice. Picking a non-descript variable such as X may confuse you later in the problem when you find you have a number, and you don't know what it is that you have found. And this is the problem people run into on word problems all the time. They solve, they get a number. But then this number, what does it have to do with the words?

What number have they actually found? That can be a frustrating thing especially when you're working under time pressure. For example, this is the beginning of a sample problem. Each week, Sarah makes $500 more than Mary, and Helen makes $700 more than Mary. 若他们的周工资总和是，诸如此类，你们可以想象这个问题还在继续。

If I pick x for the salary of one of the women, I may solve for it correctly, but when I get that number x, how will I know whether it answers the question? How will I know, was that x standing for Mary's salary? Or Sarah's salary? Or Helen's salary? In other words, it's very easy to get confused.

You'd avoid all that confusion if you just used S, M, and H. Those would be very good names for the weekly salaries of Sarah, Mary, and Helen. Some other considerations in choosing variables, sometimes it can be helpful to assign a variable for the smallest value and then express everything in terms of that. For example, in that last problem it seemed that one of the women had the smallest salary.

只给它分配一个变量，然后用这个变量来表示其他的一切可能是有意义的。 有时，将一个变量赋给目标值（问题是什么）会很有帮助。 And of course, the advantage of this is as soon as you solve for the value of that variable, you have the answer to your question.

So, some people prefer doing that. If all the quantities in the problem relate to a single quantity, make this conceptually central quantity the variable. And I'll show an example of this in a moment. 在这里，这是一个很好的例子。我会说暂停视频，思考这个问题，然后 then we'll talk about how to solve it.

好的,所以山姆g时,他的车因停车而被罚款ave Joe and Peter a ride. So they decided to help Sam pay the fine, very nice of them. 乔交的罚款比四分之一还多3美元，彼得交的罚款比三分之一还少3美元， leaving Sam $4 less than half the fine to complete the payment. How much did sam pay?

Wow. Well first of all notice that everything there is expressed in terms of the fine. So in other words, the fine, that's the conceptually central concept in every variable, how much each individual paid is related to some fraction of the fine. So it makes the most sense to say that our single variable is gonna be the fine itself, call it F for the fine.

And then we can say right away that Joe's share was (F/4)+3. Peter's share is (F/3)-3, and Sam's share was (F/2)-4. And of course if we add all these up, they should add up to the fine. So, we add them, and then, turns out that it is very easy to clear all the fractions, just by multiplying by 12. We multiply by 12.

We do a little math. And we get that the fine is 48. Now, we haven't answered the question yet. That's the price of the fine. 所以，现在我们必须回答，萨姆付了多少钱？48的一半是24。

So, that means Sam paid $4 less than that. Sam paid $20. 总之，不要使用泛型变量。选择有助于跟踪数字的变量。 Sometimes it helps to choose the smallest value as the variable, especially if everything else is related to that smallest value.

有时选择目标值作为变量会有所帮助。如果所有的量都和一个量有关， 选择该数量作为变量。我建议你在练习单词的时候， solve a word problem one way and then go back and assign variables another way. And solve it again using a different combination of variables.

你自己做个实验，这样你就有了感觉。在不同的问题中以不同的方式分配变量是什么感觉？ And that's how you build intuition for what works best for you.