EQN-03-08

Translating Word Problems into Equations

Name the unknown, build an equation from the sentence, and solve — the bridge between words and algebra.

~5 min read•Difficulty 2/5

" A number and its double" \to x and 2 x

"Three consecutive integers" \to x, x + 1, x + 2

" 5 more than twice a number" \to 2 x + 5

" A is 3 times as old as B " \to A = 3 B

"The sum of three consecutive integers is 48."

x + (x + 1) + (x + 2) = 48

3 x + 3 = 48 \to 3 x = 45 \to x = 15 \to the integers are 15, 16, 17.

If the answer choices are numbers, you can test them in the original sentence instead of building the equation — often faster on the GAT-E.

Worked examples

Example 1 (difficulty 2/5)

A number increased by 7 equals three times the number. What is the number?

◎ Predict the answer first:

Example 2 (difficulty 2/5)

Sara is 4 years older than Omar. The sum of their ages is 30. How old is Omar?

◎ Predict the answer first:

Always state clearly what x represents before writing the equation.
Consecutive integers are $x, x + 1, x + 2$ ; consecutive evens/odds are $x, x + 2, x + 4.$
If the choices are numbers, backsolving by testing them can beat full algebra.

Writing "3 times as old as B" as

B = 3 A

Why: The names are placed in reading order.

Fix: The older one equals

3 \times

the younger

: A = 3 B .

Solving for x but answering the wrong quantity

Why: x may be an intermediate, not the asked value.

Fix: Re-read what is asked and convert x back to it.