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 gym option costs less per class for seven classes. the high school option costs less per class for seven classes. the gym option costs less per class for six classes. the high school option costs less per class for six classes.

Explanation:

Step1: Define cost functions

Let \( n \) be the number of classes.
High school cost: \( C_{hs} = 20 + 10n \), average cost per class: \( \frac{20 + 10n}{n} = \frac{20}{n} + 10 \).
Gym cost: \( C_{gym} = 50 + 5n \), average cost per class: \( \frac{50 + 5n}{n} = \frac{50}{n} + 5 \).

Step2: Test \( n = 6 \)

High school average: \( \frac{20}{6} + 10 \approx 3.33 + 10 = 13.33 \).
Gym average: \( \frac{50}{6} + 5 \approx 8.33 + 5 = 13.33 \) (equal, so options C/D wrong).

Step3: Test \( n = 7 \)

High school average: \( \frac{20}{7} + 10 \approx 2.86 + 10 = 12.86 \).
Gym average: \( \frac{50}{7} + 5 \approx 7.14 + 5 = 12.14 \).
Gym average (\( 12.14 \)) < High school (\( 12.86 \)) for \( n = 7 \).

Answer:

The gym option costs less per class for seven classes.