Concept 1

Solve non-routine, multi-step problems that combine multiple topics.

Core Idea

When an ACT problem combines topics, do not try to solve everything at once. Separate the relationships first, then use the output of one step as the input to the next.

Understanding

Do not solve everything at once. Break the problem into linked steps and keep the handoff visible.

These questions often mix geometry with algebra or rates with proportions. The hard part is usually turning one result into the input for the next step.

  • Name the pieces of information you actually have.
  • Write one relationship for each clue.
  • Solve in the order that reveals the requested quantity.
  • Substitute back to confirm the final answer.

Step by Step

  1. Identify the separate math ideas in the stem before calculating.
  2. Assign variables and write one equation or expression for each clue.
  3. Solve the linked steps in an order that reveals the requested quantity.
  4. Substitute back into the original relationships to confirm the final answer.

Misconceptions

  • Solving only one relationship and forgetting the second condition.
  • Stopping at an intermediate value even though the question asks for a different quantity.
  • Using the right formula but attaching the wrong unit to the result.
Question

Worked Example

A rectangular stage has perimeter 46 feet. Its length is 5 feet greater than twice its width. What is the area of the stage, in square feet?

Select an answer to see the explanation