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:

\[ \boxed{10} \]