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All courses Math I · A-CED.3 3 of 59
Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.

Write a single inequality constraint for a budget, capacity, or time limit

Problem
You can spend at most 60 dollars on shirts costing 12 dollars each. Write a single inequality constraint.
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Hint

Multiply the cost per shirt by the number of shirts, then match “at most” with the correct inequality symbol.

“At most” means the total can be less than or equal to the limit.

Solution walkthrough

01

Identify the variable

\[s~=~\text{number}~\text{of}~\text{shirts}\]

The variable s counts how many shirts can be bought.

02

Write the total cost expression

\[12s\]

Each shirt costs 12 dollars, so s shirts cost 12s dollars.

03

Use the phrase “at most”

\[\le~60\]

At most 60 dollars means the total cost must be less than or equal to 60.

04

Write the inequality

\[12s~\le~60\]

Combining the cost expression with the limit gives the correct constraint.

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Another way

  1. You can read the inequality in words: “12 times the number of shirts is no more than 60.”

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Common mistake

A common mistake is to use ≥ instead of ≤. The phrase “at most” means the total cannot go above the limit.