Solving problem

Question

Fitkick charges $120 for membership plus $25 per month. RebelWell charges $60 for membership plus $35 per month. For how many months is RebelWell the less expensive option?

thank you!

Answer 1

It's not an equality you are trying to find. You are instead looking to solve for the highest number of months such that RebelWell still costs less total dollars than FitKick. Not "equal" or "less than equal"

120 + 25x > 60 + 35x is what you really need to solve.

120 - 60 > 35x - 25x

60 > 10x

6 > x

Or flip it around, x < 6

Since you're paying in whole month increments, it's fair to assume the answer has to be an integer. The integer next less than x is 5.

I propose 5 is the better answer. They are EQUAL at $270 in the 6th month, but that's not what the question is asking for.

Answer 2

120 + 25x = 60 + 35x is the default equation to set up here, where x represents the number of months past the first month. The idea is that you want to see when these two memberships end up being equal. Until that point, Fitkick is clearly more expensive, as it has double the initial cost. However, its increase in cost (a.k.a. rate of change) is smaller so it will eventually be cheaper.

To solve, subtract 60 from both sides of your equation and then subtract the 25x from both sides of the equation. So now...

60 = 10x

6 = x

Assuming that the first month is only 120 dollars, this would mean that the first 6 months are cheaper.