Casey wants to buy a gym membership.

Question

Casey wants to buy a gym membership. One gym has a $160 joining fee and costs $30 per month. Another gym has no joining fee and costs $70 per month. When would Casey pay the same amount to be a member of either gym? How much would he pay?

Answer 1

Hi John! You can solve this problem by writing out two systems of equations.

Let's call the costs of the two different gyms y and x. We know gym y has a $160 fee and costs $30 per month. As an equation, that would look like this:

y = $160 + $30(month).

The equation for the cost of gym x is similar, except it has no joining fee and costs $70 per month. That means

x = $0 + $70(month).

To make our equations easier to solve, let's just write the month as m. We then get:

y = 160 + 30 m

x = 70m

We want to know when the two gyms (x and y) cost the same! That means y = x. To figure out out the month, we just set the equations equal to each other and solve.

160 + 30m = 70m

160 = 40m

m = 4.

This means the costs are equal in the fourth month.

But what is this amount? We can plug m = 4 back into either equation to figure this out.

x = 70m

x = (70)(4)

x = $280.

Hope this helped!