Decoding SAT Word Problems

The College Board has said that the new SAT will include more “real world” questions, particularly on the math section. Some questions will ask you to interpret data in a chart, graph, table, or scatter plot. Other questions will ask you to turn a paragraph of information into an equation or an expression.

When it comes to word problems, it’s not enough to understand that if 4x = 20, then x = 5. You need to understand that if 20 students divide themselves into equal groups of 4, then there are 5 students in each group. Problems like these test your reading comprehension skills as much as your math skills.

The following keywords can help you quickly identify what you’re being asked to do.

Addition Subtraction Multiplication Division Equals Fraction Percent
Increased by Decreased by Of Out of Is/Are/Was/Were Denominator percent of
More than Minus Times Ratio of Gives Numerator Percent change
Combined Less than/fewer than Product of Percent of Yielded Mixed fraction Initial value
Total of Difference between/of Increased Per Earned Equivalent Percent increase/decrease
Sum Decreased by a factor of Row 1 col 3 content Sold for Graphical
Added to Numerical

 

Let’s try a sample problem:

The beginning balance in a bank account is k dollars. Each month $10 is withdrawn from the account. If no additional money is added to the account and the ending balance is $500 after 15 months, what is the the value of k?

a) 150

b) 350

c) 650

d) 450

When faced with a problem like this one, these four helpful steps can help you find the answer.

Step 1: Understand the Question

Sometimes the most confusing part of word problems is understanding exactly what the problem is asking. Read the problem carefully, underlining crucial information if necessary.

In this particular question, we’re looking for the value of k, the original balance in the bank account.

 

Step 2: Translate the Information into an Equation

Once you understand the question being asked, you can use the pieces of information to create an expression that will help you solve for the answer.

We know that after 15 months, the account had $500. We also know that the owner of the account withdrew $10 each month.

So k is $10 multiplied by 15 months, plus the $500 remaining after 15 months.

So k = 500 + 10(15).

We can rewrite this as k – 10(15) = 500

 

Step 3: Solve the Equation

Now that you have the expression, you can solve the equation as you would an ordinary math problem.

k – 10(15) = 500.

k – 150 = 500

k = 500 + 150

k = 650

 

Step 4: Plug in the Answer

Once you’ve solved the equation, you should go back to the original question to double check that you’re answering the question being asked. In this case, the original question was:

The beginning balance in a bank account is k dollars. Each month $10 is withdrawn from the account. If no additional money is added to the account and the ending balance is $500 after 15 months, what is the the value of k?

So after translating the problem into an equation and solving the equation, we found that the beginning balance in the bank account was $650. After withdrawing $10 each month for 15 months, the ending balance is indeed $500.

Word Problems can seem intimidating but the trick is to distill them down to their individual parts. If you follow these four steps as you work through word problems, you’ll be sure to do well.