Question

sarah is considering purchasing a monthly membership for her local gym, which costs $75 per month plus an additional $8 per class attended. alternatively, she can pay $12 per class without any membership fee. sarah wants to determine how many classes she would need to attend in a month for the monthly membership to be cheaper than paying per class.
a) write an inequality to model this situation.
b) solve your inequality to find out how many classes sarah would need to attend for the monthly membership to be the better option.
c) write the answer to sarahs problem, using a complete sentence in context.

Explanation:

Step1: Define cost expressions

Let $x$ be the number of classes. Cost of membership is $75 + 8x$, cost per - class is $12x$. Inequality is $75+8x<12x$.

Step2: Solve the inequality

Subtract $8x$ from both sides:
$75+8x - 8x<12x - 8x$
$75 < 4x$
Divide both sides by 4:
$\frac{75}{4}$x > 18.75$

Answer:

a) The inequality is $75 + 8x<12x$.
b) The solution of the inequality is $x>18.75$.
c) Sarah would need to attend more than 18.75 (or 19 or more) classes in a month for the monthly membership to be the better option.