Be Strong Gym currently has 3,190 members and has been losing 30 members each month. Engage Fitness, a newer gym across town, currently has 1,840 members and has been gaining 20 members each month.

Question

If these trends continue, how long will it take for the two gyms to have the same number of members?

Answer 1

Let \( t \) represent the number of months from now.

For Be Strong Gym, the number of members after \( t \) months will be: \[ 3190 - 30t \]

For Engage Fitness, the number of members after \( t \) months will be: \[ 1840 + 20t \]

We want to find the time \( t \) when the two gyms have the same number of members: \[ 3190 - 30t = 1840 + 20t \]

Now, we will first combine like terms. Add \( 30t \) to both sides: \[ 3190 = 1840 + 50t \]

Next, subtract \( 1840 \) from both sides: \[ 3190 - 1840 = 50t \] \[ 1350 = 50t \]

Now, divide both sides by \( 50 \) to solve for \( t \): \[ t = \frac{1350}{50} = 27 \]

Thus, it will take 27 months for the two gyms to have the same number of members.