Rosa pays a monthly membership fee at a gym. She also pays $5 for each cycling class she takes. In May, she took 4 cycling classes and her total cost for the month was $55. In June, Rosa’s total cost was equal to twice the membership fee. How many cycling classes did Rosa take in June?

Question

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Answer 1

Let \( m \) be the monthly membership fee.

In May, Rosa took 4 cycling classes, so her total cost can be expressed as:

\[ \text{Total Cost} = m + 5 \times 4 \]

This simplifies to:

\[ \text{Total Cost} = m + 20 \]

We know from the problem that this total cost was $55, so we can set up the equation:

\[ m + 20 = 55 \]

Solving for \( m \):

\[ m = 55 - 20 = 35 \]

So the monthly membership fee is \( m = 35 \).

In June, her total cost was equal to twice the membership fee:

\[ \text{Total Cost in June} = 2m = 2 \times 35 = 70 \]

Let \( c \) represent the number of cycling classes Rosa took in June. Therefore, her cost in June can be expressed as:

\[ 70 = m + 5c \]

Substituting \( m = 35 \):

\[ 70 = 35 + 5c \]

To find \( c \), we rearrange the equation:

\[ 70 - 35 = 5c \] \[ 35 = 5c \] \[ c = \frac{35}{5} = 7 \]

So, Rosa took 7 cycling classes in June.

The answer is 7.