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Question

Difficulty: EasyLinear Inequalities in One Variable

A gym membership costs $35\$35 per month plus an additional $5\$5 per fitness class attended. If a member wants to spend at most $65\$65 in a single month, what is the maximum number of fitness classes the member can attend?

Answer: 6 classes

Answer

The maximum number of fitness classes the member can attend is 66.
Let cc represent the number of classes. The inequality representing the budget constraint is 35+5c≤6535 + 5c \le 65. Subtracting 3535 from both sides of the inequality yields 5c≤305c \le 30. Dividing both sides by 55 yields c≤6c \le 6. Since the number of classes must be a whole number, the maximum number of classes the member can attend is 66.

Step-by-Step Solution

1
Set up the inequality representing the situation.
35+5c≤6535 + 5c \le 65
The cost of the membership is a fixed $35\$35 plus $5\$5 per class cc, and this total must not exceed $65\$65.
2
Subtract 3535 from both sides of the inequality to isolate the variable term.
5c≤305c \le 30
Isolating the term with the variable allows us to solve for cc.
3
Divide both sides by 55 to find the solution range for the number of classes.
c≤6c \le 6
Dividing by the coefficient of the variable gives the upper limit for the number of classes.

Key Concept

Solving one-variable linear inequalities in a real-world context.
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Topics

Linear Inequalities in One Variable

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