Question

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

# 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 \( C = 6 \)