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