Question

Casey wants to a gym membership one gym has $100 joining fee and costs $30 per month. Another gym has no joining fee and costs $50 per month. When would Casey pay the same to be a member of either gym? How much would he pay?

Answer 1

Casey would pay the same to be a member of either gym for a number of months equal to 5 and he would pay $250

Explanation:

Let

x ----> the number of months

y ----> the total cost in dollars

we know that

The linear equation in slope intercept form between two variables x and y is equal to

`y=mx+b`

where

m is the slope or unit rate

b is the y-intercept or initial value of the linear equation

In this problem we have

First Gym

The slope or unit rate is equal to
`m=\$30\ per\ month`

The y-intercept or initial value is
`b=\$100` ----> joining fee

so

`y=30x+100` ----> equation A

Second Gym

The slope or unit rate is equal to
`m=\$50\ per\ month`

The y-intercept or initial value is
`b=\$0` ----> joining fee

so

`y=50x` ----> equation B (proportional relationship)

equate equation A and equation B

`50x=30x+100`

solve for x

`50x-30x=100`

`20x=100`

`x=5\ months`

Verify

For x=5

First Gym

`y=30(5)+100=\$250`

Second Gym

`y=50(5)=\$250`

therefore

Casey would pay the same to be a member of either gym for a number of months equal to 5 and he would pay $250