The surf instructor has an initial fee of $12 and charges $8 per hour for lessons, which is represented by the equation y = 8x + 12, where x is the number of hours and y is the total cost. The instructor gives 32 hours of lessons a month to Sandra and 24 hours of lessons a month to Bela. What is the total amount the instructor makes in a month?

Question

Sandra: y = 8 (32) + 12. y = 256 + 12. y = 268. The instructor receives 268 dollars a month from Sandra.
The instructor makes $
a month.

Answer 1

To find the total amount the instructor makes in a month from both Sandra and Bela, we first calculate the amount the instructor earns from each student, as you've started with Sandra.

Calculation for Sandra:

1. Equation: \( y = 8x + 12 \)
2. Substituting Sandra's hours (\( x = 32 \)): \[ y = 8(32) + 12 \] \[ y = 256 + 12 \] \[ y = 268 \] Total from Sandra: $268

Calculation for Bela:

1. Substituting Bela's hours (\( x = 24 \)): \[ y = 8(24) + 12 \] \[ y = 192 + 12 \] \[ y = 204 \] Total from Bela: $204

Total Amount Instructor Makes in a Month:

Now we add the amounts from both Sandra and Bela. \[ \text{Total} = 268 + 204 \] \[ \text{Total} = 472 \]

The instructor makes $472 a month.