Ask a New Question
Menu

Part A

Devin pays $30 to be a member of the Fox Lake Gym. Each boxing class costs him $2. Jared is not a member of the Gym, and it costs him $5 for the same class. Write an equation to model the situation.

A
30+5c=2c

B
30=2c+5c

C
2+30c=5c

D
30+2c=5c

Part B

How many classes would it take for Devin's total cost to equal Jared's total cost?

classes

1 answer

To model the situation, let's define the variables:

  • Let \( c \) represent the number of boxing classes.

Part A:

Devin's cost as a member of the gym is made up of his membership fee plus the class fees:

  • Devin's total cost = Membership fee + (Cost per class * Number of classes)
  • Devin's total cost = \( 30 + 2c \)

Jared, who is not a member, pays only for the classes:

  • Jared's total cost = (Cost per class * Number of classes)
  • Jared's total cost = \( 5c \)

The correct equation representing the situation where Devin's total cost is equal to Jared's total cost is:

\[ 30 + 2c = 5c \]

Thus, the correct answer is D: \( 30 + 2c = 5c \).

Part B:

To find out how many boxing classes it would take for Devin's total cost to equal Jared's total cost, we can solve the equation \( 30 + 2c = 5c \):

  1. Subtract \( 2c \) from both sides: \[ 30 = 5c - 2c \] \[ 30 = 3c \]

  2. Divide by 3: \[ c = \frac{30}{3} = 10 \]

So, it would take 10 classes for Devin's total cost to equal Jared's total cost.