Anna-Maria H. answered • 6d

Enthusiastic Tutor Specializing in Math and ACT Prep

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!

Anna-Maria H.

6d

John H.

Thanks! This really helped me out!6d