Charlie and Caleb are personal trainers. They each charge a one-time consultation fee, and an hourly rate. Charlie charges a $18 consultation fee, plus $12 per hour. Caleb charges a $36 consultation fee, plus $6 per hour.

Question

Write an equation that represents y, the total amount Charlie charges her clients after the consultation fee and x hours of personal training.
Good work!
Complete the table below with the amount, y, that Charlie charges his clients in total with the consultation fee and various hours of personal training. You can solve on paper and then enter your answer on Zearn.
y = 18 + 12x

Hours (x) Amount charged (y)
3
6
9
You got it!
Next, graph the points you just found on the coordinate plane to show the relationship between hours and the amount that Charlie charges.
Hours (x) Amount charged (y)
3 54
6 90
9 126
You got it!
Now, consider the other personal trainer, Caleb. Write an equation that represents the total amount Caleb charges his clients, y, after the consultation fee and x hours of personal training.
Excellent!
Complete the table below with the total amount, y, that Caleb charges his clients in total with the consultation fee and various hours of personal training. You can solve on paper and then enter your answer on Zearn.
y = 36 + 6x

Hours (x) Amount charged (y)
3
6
9

Answer 1

To calculate the total amount Caleb charges using his equation \( y = 36 + 6x \), we will fill in the table for various hours of personal training (x):

Caleb's Charges Calculation

1. When \( x = 3 \): \[ y = 36 + 6(3) = 36 + 18 = 54 \]

2. When \( x = 6 \): \[ y = 36 + 6(6) = 36 + 36 = 72 \]

3. When \( x = 9 \): \[ y = 36 + 6(9) = 36 + 54 = 90 \]

Complete Table for Caleb

| Hours (x) | Amount charged (y) | |-----------|---------------------| | 3 | 54 | | 6 | 72 | | 9 | 90 |

Summary

1. Caleb's equation is \( y = 36 + 6x \).
2. The amounts charged for 3, 6, and 9 hours of training are 54, 72, and 90 respectively.