Question

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

Answer 1

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.