Compare Proportions from Graphs & Equations Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade
A membership at Gym A costs $50 for 5 months. A membership at Gym B down the street costs $40 for 3 months. You write two
equations in the form of y = ka to try and figure out which membership would be cheaper for a year. What is the value of k for the
cheaper membership? (1 point)

Answer 1

To find the value of k for the cheaper membership, we need to compare the costs of both memberships for a year.

Membership at Gym A:
Cost for 5 months = $50
Cost for 1 month = $50/5 = $10
Cost for 12 months = $10 * 12 = $120

Membership at Gym B:
Cost for 3 months = $40
Cost for 1 month = $40/3 ≈ $13.33
Cost for 12 months = $13.33 * 12 ≈ $160

Since the cost for 12 months at Gym A is $120 and the cost for 12 months at Gym B is $160, we can see that the equation for Gym A is y = 10a and the equation for Gym B is y = 13.33a.

To determine the value of k for the cheaper membership, we compare the coefficients of a (the number of months). The smaller coefficient represents the cheaper membership.

Therefore, the value of k for the cheaper membership is 10.