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?

Muscles, a membership-only gym is hoping to open a new branch in a small city in pennsylvania that currently has no fitness centers. according to their research approximately 12,600 residents live within driving distance of the gym. muscles sends out surveys to a sample of 300 randomly selected residents in this area (all of who respond) and finds that 40 residents say they would visit a gym if one was located in their area. based on the past survey research, muscles estimates that approximately 30% of these respondents would actually join the gym if they opened one in the area. based on this information and the results of the sample survey, about how many residents should muscles expect to join its new branch? a) 134 b) 504 c) 1,680 d) 3,780

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