Solving Word Problems on the SAT

In this lesson, you'll learn the 2-step process for tackling word problems on the SAT and get some hints for how to avoid common word problem pitfalls, like tricky language and mismatched units.

Word Problems

On the SAT, word problems are math problems that add an extra layer of difficulty by hiding the numbers under a layer of words. Once you've actually gotten down the math, it's often quite simple. The problem is getting to the numbers in the first place.

In this lesson, you'll learn how to break these problems down into two manageable steps: convert and complete. Instead of trying to solve directly from the words, you'll first convert the words to numbers; after that, you should be able to complete the question just like any other math problem on the test.

Step 1: Convert

Why are word problems difficult? It's not because the math is really that tough. It's because the math is hidden under a huge paragraph of text. This gives us a clue about how to solve them. Step one is always to convert the question from words into numbers.

Don't try to look at the words and solve the problem in your head or intuitively figure out the answer. Instead, carefully extract all the numbers you can from the problem, write everything down neatly in one place and then start worrying about the math. Let's take an example problem to show you how it's done.

Working all together at the same time, Martha, Susanne and Tammy complete 28 jobs in 2 hours. Tammy works twice as fast as Martha. If Susanne is responsible for completing 10 of the jobs, how many jobs does Tammy complete?

1. 6
2. 10
3. 12
4. 16
5. 22

That's a lot of text. Let's see what we can dig out of this one.

First, we'll start by assigning variables. We'll use M to stand for the number of jobs that Martha worked, and Sfor the number of jobs that Susanne worked and T for the number of jobs that Tammy worked. We already know that S = 10 because our problem tells us that Susanne did 10 jobs. We also know that the three girls together did 28 jobs, so we can say that M + S + T = 28.

And we know that Tammy works twice as fast as Martha. Since each of the girls worked for the same amount of time (two hours), this tells us that Tammy did twice as much work, or twice as many jobs, as Martha. So we can write T = 2M. The number of Tammy's jobs is twice the number of Martha's jobs.

At this point, we haven't solved any equations yet; we've simply dug up the numbers that were hiding in the word problem and written them down all neatly together so we can see what we're working with. In other words, we've converted this one from a word problem into a regular old math problem - and now, suddenly, it doesn't look so bad!

Step 2: Complete

Now it's time to move on to step two: completing the problem. First of all, we know that S = 10, so we can start by plugging that in to get rid of one of these variables. Just two variables left. Doesn't that look better already? Now we can simplify this equation by subtracting 10 from both sides to get M + T = 18. Using the other equation, we plug in 2M for T, and we can solve to find that M = 6.

In the context of our problem, this means that Martha did six jobs. Tammy did twice as many, so Tammy must have done 12 jobs, and the correct answer is C. You can see how the problem gets a lot easier as soon as we get rid of the words and start looking at just the numbers. It's really a fairly simple algebra problem - without the words, this would have been an easy question. That's the reward of using the 2-step method to complete word problems. Once you do the hard work of wading through the sentences, the actual math itself is a breeze.

Conversion Tips

Now let's briefly go over some tips to help you convert accurately and efficiently. This example was pretty straightforward, but not all of the questions are, so watch out for these common stumbling blocks.

First up, whenever you see 'of,' think 'multiply.' This is especially common with fractions. One-third of nine means one-third times nine.

Next, be wary of 'less than.' This is one of the SAT's favorite tricks because it trips up everyone. If you see something like 'Jim's speed is three miles per hour less than Steve's speed,' it's very tempting to write out the numbers from left to right, J = 3 - S.

But this isn't correct. 'Three miles per hour less than Steve's speed' means that you take Steve's speed and subtract three from it. A correct way of putting this sentence into numbers would be J = S - 3. If you're a visual learner, you can think of this like a big spiral. To translate from words into math, just follow the path of the spiral from Jim all the way out to Steve and finally back to three.

Finally, pay attention to unit tricks. The test writers love to throw you curve balls, like times in minutes but speeds in miles per hour. It's your job to recognize that the units are different and to convert everything to one set of units before you start working on the problem.