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.

Answer 1

Let's start by confirming the total cost for Sandra:

Given the equation \( y = 8x + 12 \):

• For Sandra, \( x = 32 \): \[ y = 8(32) + 12 = 256 + 12 = 268. \] So, Sandra pays $268 for her lessons.

Now, let's calculate the total cost for Bela, who receives 24 hours of lessons:

Using the same equation:

• For Bela, \( x = 24 \): \[ y = 8(24) + 12 = 192 + 12 = 204. \] So, Bela pays $204 for her lessons.

Now, to find the total amount the instructor makes in a month from both Sandra and Bela, we will add their payments together: \[ \text{Total Amount} = \text{Pay from Sandra} + \text{Pay from Bela} = 268 + 204 = 472. \]

Therefore, the instructor makes a total of $472 in a month.