A karate academy charges a monthly membership fee plus an additional fee per class. You must show ALL work to earn full credit.

Question

# of classes 1,5,8,14,20
total cost 36,60,78,114,150
What is the charge per class?

Answer 1

To find the charge per class and the monthly membership fee, we can set up a system of equations based on the provided data.

Let:

• \( M \) = monthly membership fee
• \( C \) = charge per class

We have the following data points based on the number of classes and total cost:

• For 1 class: \( M + 1C = 36 \)
• For 5 classes: \( M + 5C = 60 \)
• For 8 classes: \( M + 8C = 78 \)
• For 14 classes: \( M + 14C = 114 \)
• For 20 classes: \( M + 20C = 150 \)

We can use the first two equations to find \( M \) and \( C \).

1. From the first equation: \[ M + 1C = 36 \quad \text{(i)} \]

2. From the second equation: \[ M + 5C = 60 \quad \text{(ii)} \]

Now we can subtract equation (i) from equation (ii): \[ (M + 5C) - (M + 1C) = 60 - 36 \] This simplifies to: \[ 4C = 24 \] Now, divide both sides by 4: \[ C = 6 \]

Now that we have \( C \), we can substitute it back into equation (i) to find \( M \): \[ M + 1(6) = 36 \] This simplifies to: \[ M + 6 = 36 \] Subtracting 6 from both sides gives: \[ M = 30 \]

Thus, the monthly membership fee \( M \) is 30, and the charge per class \( C \) is 6.

Answer: Charge per class \( C = 6 \)