Question

Set up and solve a system of equations to solve the problem. Casey wants to buy a gym membership. One gym has a $100 joining fee and costs $35 per month. Another gym has no joining fee and costs $60 per month. When would Casey pay the same amount to be a member of either gym? How much would he pay?

A) Casey would pay the same amount after 4 months, $220 in total.

B) Casey would pay the same amount after 3 months, $180 in total.

C) Casey would pay the same amount after 5 months, $300 in total.

D) Casey would pay the same amount after 2 months, $120 in total.

Answer 1

To solve the problem, we set up a system of equations using x as the number of months. By setting the two equations equal to each other and simplifying, we find that Casey would pay the same amount after 4 months, totaling $220.

Step-by-step explanation:

To determine when Casey would pay the same amount to be a member of either gym, we can set up a system of equations.

Let x represent the number of months.

For the first gym, Casey would pay a total of $100 (joining fee) + $35x (monthly cost).

For the second gym, Casey would pay a total of $0 (joining fee) + $60x (monthly cost).

Setting these two equations equal to each other: 100 + 35x = 60x.

Simplifying the equation, we get: 100 = 25x.

Dividing both sides of the equation by 25, we find x = 4.

Therefore, Casey would pay the same amount after 4 months, which is a total of $220.