Question

A gym offers two different membership options. In the 1st option, new members pay a one time fee of $50 and a monthly fee of $30. In the 2nd option, members pay a one time fee of $100 and a monthly fee of $20. In this activity you will use substitution to solve for one variable in this system of equations and find the number of month it will take for the total cost of the membership be the same for both plans.

To find out when the cost will be equal, you will need to solve for m (months) using substitution. Substitute the expression for the cost from the first equation into the cost, c (total membership cost), In the second equation.

Answer 1

This is the sample answer BUT I rephrased it for you.

Explanation:

c = 30m + 50 (1)

c = 20m + 100 (2)

Equation (2) is created by substituting the value of c from equation (1) into equation (2).

30m + 50 = 20m + 100

Answer 2

m = 5

Explanation:

The cost of membership in the 1st option is ...

c = 50 + 30m

The cost of membership in the 2nd option is ...

c = 100 + 20m

__

Solving by substitution, we get ...

50 +30m = 100 +20m . . . . substitute for c

10m = 50 . . . . . . . . . . . . . . . subtract (50+20m)

m = 5 . . . . . . . . . . . . . divide by 10

It will take 5 months for the cost of membership to be the same for both plans.