Question

using substitution to solve a system of equations
anna wants to take fitness classes. she compares two gyms to determine which would be the best deal for her. fit fast charges a set fee per class. stepping up charges a monthly fee, plus an additional fee per class. the system of equations models the total costs for each.
$y = 7.5x$
$y = 5.5x + 10$
1 substitute $7.5x = 5.5x + 10$
how many classes could anna take so that the total cost for the month would be the same?
\boxed{} classes
what is the total monthly cost when it is the same for both gyms?
$\boxed{}$

Explanation:

Step1: Isolate the x-term

Subtract $5.5x$ from both sides:
$7.5x - 5.5x = 10$

Step2: Simplify left side

Calculate the difference of coefficients:
$2x = 10$

Step3: Solve for x

Divide both sides by 2:
$x = \frac{10}{2} = 5$

Step4: Find total cost y

Substitute $x=5$ into $y=7.5x$:
$y = 7.5 \times 5 = 37.5$

Answer:

5 classes
$\$37.50$