Question

naomi wants to take yoga classes. she can take classes at the high school for a one - time fee of $20 plus $10 per class. she can join the local gym for $50 and take classes for $5 per class. which statement is true about the average cost for the two options?
the high school option costs less per class for six classes.
the gym option costs less per class for six classes.
the high school option costs less per class for seven classes.
the gym option costs less per class for seven classes.

Explanation:

Step1: Define cost functions

Let $n$ = number of classes.
High school total cost: $C_h = 20 + 10n$
Gym total cost: $C_g = 50 + 5n$
Average cost: $\text{Average Cost} = \frac{\text{Total Cost}}{n}$

Step2: Calculate avg cost for 6 classes

High school avg: $\frac{20 + 10(6)}{6} = \frac{80}{6} \approx 13.33$
Gym avg: $\frac{50 + 5(6)}{6} = \frac{80}{6} \approx 13.33$

Step3: Calculate avg cost for 7 classes

High school avg: $\frac{20 + 10(7)}{7} = \frac{90}{7} \approx 12.86$
Gym avg: $\frac{50 + 5(7)}{7} = \frac{85}{7} \approx 12.14$

Answer:

D. The gym option costs less per class for seven classes.