Practice Constraints in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Conditions or limitations that restrict which values a variable or solution can take in a problem.

You can't spend more money than you have—that's a constraint.

Example 1

medium
You have \50 to spend on notebooks (\3 each) and pens (\$2 each). Write the constraint inequality and find a valid combination.

Example 2

hard
A farmer plants corn (\200/acre profit) and soybeans (\150/acre profit) on at most 100 acres, with at least 20 acres of corn. Write the constraints and find the profit-maximizing allocation.

Example 3

medium
A box must hold at least 10 items but no more than 25 items. Write this as a compound inequality and list two valid values.

Example 4

hard
A recipe needs at least 2 cups of flour and no more than 5 cups total of flour and sugar combined. If you use 3 cups of flour, what is the range of sugar cups?
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