Question

Ashley may purchase an annual gym membership for $ 1,295 . She also has the option to pay month-to-month, for a monthly fee of $ 140 . What is the minimum number of months that Ashley must be a member in order for the annual membership to be less than the cost of paying fees from month-to-month?

Answer 1

To determine the minimum number of months Ashley must be a member for the annual membership to be less than the cost of paying month-to-month, we will set up an inequality.

Let \( m \) be the number of months Ashley is a member. The cost of the month-to-month membership is:

\[
140m
\]

The cost of the annual membership is:

\[
1295
\]

We want to find the smallest integer \( m \) such that:

\[
1295 < 140m
\]

To solve for \( m \), we first divide both sides by 140:

\[
\frac{1295}{140} < m
\]

Calculating the left side:

\[
\frac{1295}{140} \approx 9.21428571428571
\]

Since \( m \) must be an integer, we need to round up to the next whole number:

\[
m \geq 10
\]

Thus, the minimum number of months Ashley needs to be a member for the annual membership to be less expensive than the month-to-month payments is:

\[
\boxed{10}
\]