Question

PLEASE!!!

A gym offers two different membership options. In the first option, new members pay a one-time fee of $50 and a monthly fee of $30. In the second option, members pay a one-time fee of $100 and a monthly fee of $20.
Suppose c is the total membership cost for m months. The two equations that model the two membership options are c = 30m + 50 and c = 20m + 100.

Part A
1. To find out when the cost will be equal, you will need to solve for m using substitution. Substitute the expression for the cost from the first equation into the cost, c, in the second equation.

2. Solve the equation in number 1 for m

3. Would you get the same solution if you substituted the expression for cost in the second option for c in the first equation? Why?

Answer 1

9514 1404 393

Answer:

1. 30m +50 = 20m +100
2. m = 5
3. yes. symmetric property of equality.

Explanation:

1. The expression for c in the first equation is (30m+50). Substituting that for c in the equation ...

c = 20m +100

gives you ...

30m +50 = 20m +100

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2. Adding -50-20m to both sides gives ...

10m = 50

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

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3. Doing the substitution in reverse, you would substitute (20m+100) for c in the equation ...

c = 30m +50

to get ...

20m +100 = 30m +50

This is the equation of part 1 with the expressions swapped to the other side of the equal sign. The symmetric property of equality tells you that changing sides of the equal sign does not change the value of the variable(s).

You get the same solution.