Question

A fitness center opens and has a membership fee of $150 and a monthly fee of $10. Use x as the number of months and y as the total fee to create an equation. a. What is the equation for this situation? b. What is the y-intercept? What does it represent? c. What would the total cost be after 10 months?d. Would the total cost after 5 months be $50? Explain.

Answer 1

a.

Let x be the number of months we use the gym. Since the monthly fee is $10, for x number of months we are going to pay:

`10x`

To get the total fee we have to add the membership fee:

`10x+150`

Therefore, the equation that represents this situation is:

`y=10x+150`

b.

The y intercept of this equation is 150, this represents the initial fee (that is the membership fee) that we have to pay to join the gym.

c.

To calcualte the the total cost after 10 months we plug x=10 into the equation of the cost, then:

`y=10(10)+150=100+150+=250`

therefore after 10 months the total cost would be $250.

d.

After 5 months the total cost would be:

`y=10(5)+150=50+150=200`

Therefore the total cost after 5 months is not $50, this comes from the fact that we have to add the membership fee to the total cost.