Concept 7

Model relationships with equations/inequalities and translate word problems into algebra.

Translate each part of a word problem into algebra before you solve.

Core Idea

Translate the relationship sentence by sentence. One phrase usually gives the variable meaning, another gives the total, and words like at least or at most tell you whether you need an inequality.

Understanding

Rule: Word problems get easier when you stop trying to convert the whole paragraph at once. Define the variable first, then map each sentence to one algebra statement.

On ACT, the common misses are not algebra mistakes. They are translation mistakes: mixing up total and rate, reversing who has more, or using an equation when the wording actually creates an inequality.

Step by Step

  1. Define the variable first.
  2. Translate each sentence into one algebra statement.
  3. Choose an equation or inequality that matches the wording.

Misconceptions

  • Using the variable for the wrong quantity.
  • Reversing a comparison such as "5 more than twice x."
  • Writing an equation when the context says at least or at most.
Question

Worked Example

Student tickets to a play cost $9 each, and adult tickets cost $14 each. A group buys 18 tickets for a total of $207. If 𝑠 is the number of student tickets, which equation can be used to find 𝑠?

Select an answer to see the explanation