Question

when the number of classes is _____, football is less expensive

when the number of classes is _____, basketball is less expensive

football program: number of classes total cost
1 15
2 30
3 45
4 60
basketball program: y = 9x + 10

Answer 1

To determine when the costs of football and basketball programs compare, we can look at the provided details and equations.

### Football Program
From the table you provided, we can see the total cost of the football program based on the number of classes:

- 1 class: $15
- 2 classes: $30
- 3 classes: $45
- 4 classes: $60

This indicates that the cost of the football program increases by $15 for each additional class.

### Basketball Program
The cost function for the basketball program is given as:
\[ y = 9x + 10 \]
where:
- \(y\) is the total cost,
- \(x\) is the number of classes.

### Equating Costs
To find out when football is less expensive than basketball, we can set the equations equal to each other and solve for \(x\).

1. **Football Cost**: \( F(x) = 15x \)
2. **Basketball Cost**: \( B(x) = 9x + 10 \)

Set the costs equal:
\[
15x = 9x + 10
\]

### Solve for \(x\):
\[
15x - 9x = 10
\]
\[
6x = 10
\]
\[
x = \frac{10}{6} = \frac{5}{3} \approx 1.67
\]

### Conclusion
So:
- **When the number of classes is less than about 1.67 (or 1 class)**, football is less expensive.
- **When the number of classes is more than about 1.67 (or 2 classes)**, basketball becomes less expensive.

In conclusion:

- When the number of classes is **1 or fewer**, football is less expensive.
- When the number of classes is **2 or more**, basketball is less expensive.

You can also summarize it as:
- Football is less expensive for **1 class**.
- Basketball becomes less expensive starting at **2 classes**.