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 \(x\).
- Football Cost: \( F(x) = 15x \)
- 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.