Question

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. what is the system of equations representing these costs?
○ $y = 5.5x$ and $y = 7.5x + 10$
○ $y = 7.5x$ and $y = 5.5x$
○ $y = 7.5x$ and $y = 5.5x + 10$
○ $y = 7.5x + 10$ and $y = 5.5x + 10$

Explanation:

Step1: Analyze Fit Fast's cost

Fit Fast charges a set fee per class. Let \( x \) be the number of classes and \( y \) be the total cost. If the per - class fee is, say, \( 7.5 \) (we'll see from the options), the equation is \( y = 7.5x \) (since there's no monthly fee, just cost per class).

Step2: Analyze Stepping Up's cost

Stepping Up charges a monthly fee plus a per - class fee. Let the monthly fee be \( 10 \) and the per - class fee be \( 5.5 \). Then the total cost \( y \) for \( x \) classes is \( y=5.5x + 10 \) (the \( 10 \) is the monthly fee and \( 5.5x \) is the cost for \( x \) classes).

Looking at the options, the system of equations that represents this is \( y = 7.5x \) and \( y=5.5x + 10 \).

Answer:

\( y = 7.5x \) and \( y = 5.5x + 10 \) (the third option: \( y = 7.5x \) and \( y = 5.5x + 10 \))