Question

club A charge $11 for membership and $11 monthly. Club B charge $27 membership and $7 monthly. After how many many months will they charge the same? How much for each?

Answer 1

Let $m$ be the number of months. Since Club A charges $11 only one time and charges $11 per month, the total charge after $m$ months is $\ 11 + \ 11m$. Similarly, the total charge after $m$ months for Club B is $\ 27 + \ 7m$.

Since we want to find after how many months the two clubs charge the same amount, we can set those two expressions equal to each other and solve:

$\ 11 + \ 11m = \ 27 + \ 7m$
$\ 4m = \ 16$
$\bf m = 4$

So, Club A and Club B will charge the same amount after 4 months. To find how much they charge, just plug $m$ back into one of the original equations:

$\ 11 + \ 11m = \ 11 + \ 11(4) = \bf \ 55$