# PSAT Math: Linear Word Problems

On the PSAT Math Test, another way linear equations can be made to look complicated is for them to be disguised in “real-world” word problems, where it’s up to you to extract and solve an equation. When you’re solving these PSAT math problems, you may run into trouble translating English into math. The following table shows some of the most common phrases and mathematical equivalents you’re likely to see on the PSAT.

### PSAT Word Problems Translation Table

 English Math equals, is, equivalent to, was, will be, has, costs, adds up to, the same as, as much as = times, of, multiplied by, product of, twice, double, by × divided by, per, out of, each, ratio ÷ plus, added to, and, sum, combined, total, increased by + minus, subtracted from, smaller than, less than, fewer, decreased by, difference between – a number, how much, how many, what x, n, etc.

Linear word problems are made more difficult by complex phrasing and extraneous information. Don’t get frustrated—word problems can be broken down in predictable ways.

To stay organized on Test Day, use the Kaplan Strategy for Translating English into Math:

• Define any variables, choosing letters that make sense.
• Break sentences into short phrases.
• Translate each phrase into a mathematical expression.
• Put the expressions together to form an equation.

Let’s apply this to a straightforward example: Colin’s age is three less than twice Jim’s age.

• Define any variables, choosing letters that make sense: We’ll choose C for Colin’s age and J for Jim’s age.
• Break sentences into short phrases: The information about Colin and the information about Jim seem like separate phrases.
• Translate each phrase into a mathematical expression: Colin’s age = C; 3 less than twice Jim’s age = 2J – 3.
• Put the expressions together to form an equation: Combine the results to get C = 2J – 3.

This strategy fits into the larger framework of the Kaplan Method for Math: When you get to Step 2: Choose the best strategy to answer the question and are trying to solve a word problem as efficiently as possible, switch over to this strategy to move forward quickly.

The Kaplan Strategy for Translating English into Math works every time. Apply it here to a test-like example:

1. The number k can be determined in the following way: Multiply m by 2, add 3n to the result, and subtract (4m − 5n) from this sum. What is the value of k in terms of m and ?

(A) −2m − 3n

(B) −2m + 2n

(C) −2m + 8n

(D) 6m − 2n

Work through the Kaplan Method for Math step-by-step to solve this question. The following table shows Kaplan’s strategic thinking on the left, along with suggested math scratchwork on the right.

Strategic Thinking Math Scratchwork

Step 1: Read the question, identifying and organizing important information as you go

The question is asking you to solve for k in terms of m and n. You’re looking for what comes after k = .

Step 2: Choose the best strategy to answer the question

Where should you start? Go through each component of the Kaplan Strategy for Translating English into Math.

Do you need to choose variables? No, the variables are already defined for you.

How can you logically break this question down? Phrases about k and phrases about m and n are reasonable choices.

Go ahead and translate:

k can be determined”

“Multiply m by 2, add 3n to the result”

“Subtract (4m − 5n)”

Combine the results.

This doesn’t look like an exact match for any of the answer choices. Can you simplify?

Distribute the negative and combine like terms.

k
=

2m + 3n

- (4m – 5n)

k = 2m + 3n – (4m – 5n)

k = 2m + 3n – 4m + 5n

Step 3: Check that you answered the right question

Perfect! Now you have an exact match for (C).

k = -2m + 8n