Question

You are choosing between two health clubs. Club A offers membership for a fee of $12 plus a monthly fee of $28. Club B offers membership for a fee of $20 plus a
monthly fee of $26. After how many months will the total cost of each health club be the same? What will be the total cost for each club?
In __ months the total cost of each health club will be the same.

Answer 1

A has fixed one time fee of $12 and if you go to it say "m" months you pay $28 for each month, so your total cost at A is really 12 + 28m.

B has a fixed one time fee of $20 and if you go to it "m" months you pay $26 for each month, so you total cost at B is 20 + 26m.

how many months for the cost to be the same?

$\stackrel{A}{12+28m}=\stackrel{B}{20+26m}\implies 12+2m=20\implies 2m=8\implies m=\cfrac{8}{2}\implies m=4$

well, since the cost for both is the same, we can just get A's, knowing that B is the same

$12+28(4)\implies 12+112\implies 124$