Question

Brett is joining a new gym. He can join Power Plus or Heavy Hulk. At Power Plus, it will cost $34.06 per month, plus a sign-up fee of $20.00. At Heavy Hulk, it will cost $34.31, plus a sign-up fee of $32.50. Right now, Heavy Hulk is cutting their sign-up fee in half for new members. If Brett signs up at a gym today, after how many months will the cost of the memberships be the same?

A. 50
B. 12.25
C. The cost will never be the same.
D. 15

Answer 1

15

Explanation:

Let x be the number of months of membership.

Write an expression to model the cost to join Power Plus. It costs $34.18 per month, plus the $20.00 sign-up fee.

$34.18x + $20.00

Write an expression to model the cost to join Heavy Hulk. Remember that the sign-up fee is currently being cut in half, so half of $32.50 is $16.25. It costs $34.43 per month, plus the $16.25 sign-up fee.

$34.43x + $16.25

To determine how many months Brett would have to be a member for the cost to be the same at Power Plus and Heavy Hulk, create an equation using the expressions above.

$34.18x + $20.00 = $34.43x + $16.25

Solve the equation for x.

$34.18x + $20.00 = $34.43x + $16.25

$3.75 = $0.25x

15 = x

x = 15

So, Brett would have to be a member for 15 months for the cost to be the same.

Answer 2

C

Explanation:

Lets begin with making this into an equation where x is the amount of months

x must be bigger than zero for them to cross

Power Plus = 34.06x + 20

Heavy Hulk = 34.31x + 32.50

When are these equal

34.06x + 20 = 34.31x + 32.50

34.06x = 34.31x + 12.50

-0.25x = 12.50

x = -50

Since x must be higher than zero(you cant go there for minus months) the answer is C