Question

Please help ASAP!

Gym A requires a $45 initial fee and charges $12 monthly. Gym B requires an initial fee of $150 and charges $9 per month. How many months would you have to join for the cost of both gyms to be the same?
WRITE IT AS A SYSTEM! 2 EQUATIONS, 2 VARIABLES

Answer 1

Answer is 35 months for both gyms to cost the same

y = 12m + 45 equation #1
y = 9m + 150 equation #2

Substitute the y value of equation 1 in for y of equation 2 and solve

12m + 45 = 9m + 150

Subtract 9m from both sides to isolate variable

12m - 9m + 45 = 9m - 9m + 150
Combine

3m + 45 = 150

Subtract 45 from both sides to combine constants

3m + 45 - 45 = 150 - 45
Combine

3m = 105

Divide both sides by 3 to solve for m

3/3 m = 105/3

m = 35 months

Check your work. Substitute 35 for m in your equation and solve.

12m + 45 = 9m + 150
12(35) + 45 = 9(35) + 150
420 + 45 = 315 + 150
465 = 465

They equal so problem solved!