Question

Greg wants buy a gym membership. One gym cost $10 per month with a one time joining fee of $40. Another gym charges $15 per month with no joining fee. When would Greg pay the same amount to be a member at either gym? How much would he pay?

Answer 1

The cost of membership at gym A can be written as:

c

a

=

$

10

m

+

$

15

The cost of membership at gym B can be written as:

c

b

=

$

4

m

+

$

40

Where

c

g

y

m

is the cost after

m

months.

To find when the cost is equal, equate the right side of both equations and solve for

m

:

$

10

m

+

$

15

=

$

4

m

+

$

40

Next, subtract

$

15

and

$

4

m

from each side of the equation to isolate the

m

term while keeping the equation balanced:

−

$

4

m

+

$

10

m

+

$

15

−

$

15

=

−

$

4

m

+

$

4

m

+

$

40

−

$

15

(

−

$

4

+

$

10

)

m

+

0

=

0

+

$

25

$

6

m

=

$

25

Now, divide each side of the equation by

$

6

to solve for

m

while keeping the equation balanced:

$

6

m

$

6

=

$

25

$

6

$

6

m

$

6

=

$

25

$

6

m

=

25

6

m

=

4.17

At 4 months the cost of the two gym memberships will be about the same.

Explanation: