Practice Constraints in Math

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

Quick Recap

Conditions or restrictions that limit which values are allowed in a problem. Constraints narrow the set of possible solutions, such as 'x must be positive' or 'the total cannot exceed 100.'

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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