algebra 1 word problem

Question

isaac can join a gym for $20 per month, plus a one time fee of $12, or he can join gym b where he would pay $22 per month with no extra fee.

A) write an expression to figure out how much isaac would pay at each gym.

B) use your answer from A to write an equation to figure out when the two gyms would cost the same

C) solve the equation to find the number of months at which the two will be equal

all the help would be very much appreciated

Answer 1

A)

a = 20m + 12

b = 22m

B)

Set the equations equal since you want to know when the costs are the same:

22m = 20m + 12

C)

Solve:

Subtract 20m from both sides of the equation, thus combining all the like-term variables on the same side of the equals sign.

2m = 12

Divide both sides if the equation by the coefficient of m, which is 2 in this case.

m = 6

So, the costs will be the same after 6 months.

Answer 2

A) fa = 20 * m + 12 and fb = 22 * m, where m is the number of months and fa and fb are the total fees for the respective gyms after m months.

B) We want to know when fa = fb, so we can replace fa and fb with the equations from step A) to give us:

20 * m + 12 = 22 * m

C) Can you solve the equation in step B) yourself to find the value of m that makes the equation true?