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The surf instructor has an initial fee of [tex]$12$[/tex] and charges [tex]$8$[/tex] per hour for lessons, which is represented by the equation [tex]y = 8x + 12[/tex], where [tex]x[/tex] is the number of hours and [tex]y[/tex] 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?

For Sandra:
[tex]\[
\begin{array}{l}
y = 8(32) + 12 \\
y = 256 + 12 \\
y = 268
\end{array}
\][/tex]
The instructor receives [tex]$268 a month from Sandra.

For Bela:
\[
\begin{array}{l}
y = 8(24) + 12 \\
y = 192 + 12 \\
y = 204
\end{array}
\]
The instructor receives $[/tex]204 a month from Bela.

What is the total amount the instructor makes in a month?

The instructor makes [tex]$\$[/tex]268 + \[tex]$204 = \$[/tex]472$ a month.



Answer :

GinnyAnswer
To calculate the total earnings of the surf instructor, we need to consider both Sandra and Bela.

Firstly, we calculate the monthly earnings from Sandra:
[tex]\[ y = 8 \times 32 + 12 \][/tex]
[tex]\[ y = 256 + 12 \][/tex]
[tex]\[ y = 268 \][/tex]
Thus, the instructor receives [tex]$268 a month from Sandra. Next, we calculate the monthly earnings from Bela: \[ y = 8 \times 24 + 12 \] \[ y = 192 + 12 \] \[ y = 204 \] Thus, the instructor receives $[/tex]204 a month from Bela.

To find the total amount the instructor makes in a month from both students, we add the amounts from Sandra and Bela:
[tex]\[ 268 + 204 = 472 \][/tex]

Therefore, the instructor makes [tex]$\$[/tex] 472$ a month from both Sandra and Bela together.

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