Which situation is best represented by the following equation?

Question

45w + 123.95 = 753.95
A. Erica paid $753.95 for dance classes. She paid a 123.95 registration fee and $45 for each week she enrolled in the classes. What is w, the number of weeks Erica was enrolled in dance classes?
B. Erica paid 753.95 for dance classes. She paid a $45 registration fee for each week she was enrolled in the classes. What is w, the number of weeks Erica was enrolled in dance classes?
C. Erica and her sister paid $753.95 for dance classes. Erica paid $123.95 for each week she was enrolled in the classes, and her sister paid $45 for each week she was enrolled in the classes. What is w, the number of weeks Erica and her sister were enrolled in dance classes?
D. Erica paid $753.95 for dance classes. She paid $123.95 for each week she was enrolled in the classes after using a coupon that gave her $45 off the price per week what is w, the number of weeks Erica was enrolled in dance classes?
w= 14 weeks
plug in for w.

Answer 1

To analyze the equation \( 45w + 123.95 = 753.95 \), let's break down its components:

1. \( 45w \) suggests that the total cost increases by $45 for each week, indicating a weekly fee.
2. \( 123.95 \) represents a fixed cost, such as a registration fee that is paid upfront.
3. \( 753.95 \) is the total amount paid, which includes both the fixed cost and the variable cost based on the number of weeks enrolled.

Now, let's relate this equation to the options presented:

• Option A: Erica paid $753.95 for dance classes. She paid a $123.95 registration fee and $45 for each week she enrolled in the classes. What is \( w \), the number of weeks Erica was enrolled?

  • This matches perfectly with our equation since it reflects a registration fee and a weekly cost, leading us to conclude that \( w \) represents the number of weeks Erica was enrolled.

• Option B: Erica paid $753.95 for dance classes. She paid a $45 registration fee for each week she was enrolled. This would not fit the equation because it mischaracterizes the costs involved.

• Option C: Erica and her sister paid $753.95 for dance classes. This introduces a second person and changes the interpretation of the cost structure. The relationship of the variables does not match the original equation.

• Option D: Erica paid $753.95 for dance classes, but her costs are defined incorrectly by mixing in a coupon that adjusts the weekly cost. This does not align with the equation.

Thus, the situation best represented by the equation \( 45w + 123.95 = 753.95 \) is:

A. Erica paid $753.95 for dance classes. She paid a $123.95 registration fee and $45 for each week she enrolled in the classes. What is \( w \), the number of weeks Erica was enrolled in dance classes?

When you plug in \( w = 14 \):
\[ 45(14) + 123.95 = 630 + 123.95 = 753.95, \] which confirms that \( w \) represents the number of weeks enrolled.