Question

Megan is deciding between two gyms. Gym A has a one-time membership fee of $30 and a monthly cost of $10. Gym B's cost can be represented by the equation y = 15x. Which gym would be more cost-effective after x months?

A) Gym A
B) Gym B
C) They cost the same after x months
D) Not enough information to determine

Answer 1

After comparing the total costs of Gym A and Gym B over x months, Gym B is more cost-effective for periods less than 6 months, Gym A is more cost-effective for periods longer than 6 months, and both are equally cost-effective exactly at 6 months.

Step-by-step explanation:

To determine which gym, A or B, is more cost-effective after x months, we need to compare the total costs from both gyms over that period. For Gym A, the cost over x months is given by the initial fee plus the monthly cost times the number of months: Cost(A) = $30 + $10x. For Gym B, the cost over the same period is given directly by the equation y = 15x, with no initial fee.

To find out after how many months both gyms cost the same, we set the equations equal to each other:

$30 + $10x = 15x

Solving for x, we get:

$30 = 15x - 10x


$30 = 5x


x = 6

So, after 6 months, both gyms cost the same. For periods less than 6 months, Gym B is more cost-effective, and for periods longer than 6 months, Gym A is more cost-effective. Therefore, the answer to which gym is more cost-effective after x months depends on the value of x:

• For x < 6, the answer is B) Gym B.
• For x > 6, the answer is A) Gym A.
• For x = 6, the answer is C) They cost the same after x months.