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. So its cost equation is of the form \( y = mx \) (no monthly fee, just per - class fee).

Step2: Analyze Stepping Up's cost

Stepping Up charges a monthly fee plus an additional fee per class. So its cost equation is of the form \( y=mx + b\), where \( b\) is the monthly fee (\(b>0\)) and \( m\) is the per - class fee.

Step3: Match with options

• For Fit Fast (per - class fee only), the equation should be \( y = 7.5x\) (assuming the per - class fee is 7.5) or \(y = 5.5x\). For Stepping Up (monthly fee + per - class fee), the equation should have a non - zero constant term (the monthly fee) and a per - class fee.
• Looking at the options, Fit Fast has a per - class fee (so \(y=\text{per - class fee}\times x\)) and Stepping Up has a monthly fee (so \(y=\text{per - class fee}\times x+\text{monthly fee}\)).
• In option C: \(y = 7.5x\) (Fit Fast, per - class fee of 7.5) and \(y=5.5x + 10\) (Stepping Up, per - class fee of 5.5 and monthly fee of 10), which matches the description.

Answer:

C. \( y = 7.5x \) and \( y = 5.5x + 10 \)