Question

systems of linear equations word problems: medium
michael is planning to join a local gym and is researching his options. his first option, bodies in motion, charges a one - time enrollment fee of $60.00, plus an additional monthly fee of $18.00. his second option, cardio world, does not have an enrollment fee, but charges $30.00 per month. in how many months will the total cost for a gym membership at both gyms be equal?

Explanation:

Step1: Set up equations

Let $x$ be the number of months. For Bodies In Motion, the cost $C_1 = 60 + 18x$. For Cardio World, the cost $C_2=30x$.

Step2: Set costs equal

Set $C_1 = C_2$, so $60 + 18x=30x$.

Step3: Solve for $x$

Subtract $18x$ from both sides: $60=30x - 18x$, which simplifies to $60 = 12x$. Then divide both sides by 12: $x=\frac{60}{12}=5$.

Answer:

5