To find the correct equation that represents the given scenario, we'll break down the problem step by step.
Justine's total cost of the music program includes:
1. A one-time registration fee of \[tex]$45.
2. A cost of \$[/tex]9 per lesson for [tex]\( x \)[/tex] lessons.
The average cost per lesson is given to be \[tex]$12.
The total cost for \( x \) lessons can be expressed as:
\[ \text{Total Cost} = \text{Registration Fee} + (\text{Cost per Lesson} \times \text{Number of Lessons}) \]
\[ \text{Total Cost} = 45 + (9 \times x) \]
The average cost per lesson is given by the total cost divided by the number of lessons:
\[ \text{Average Cost per Lesson} = \frac{\text{Total Cost}}{\text{Number of Lessons}} \]
\[ \text{Average Cost per Lesson} = \frac{45 + 9x}{x} \]
We are told that the average cost per lesson is \$[/tex]12, so we set up the equation:
[tex]\[ 12 = \frac{45 + 9x}{x} \][/tex]
This matches one of the provided answer choices:
C. [tex]\( 12 = \frac{45 + 9x}{x} \)[/tex]
Therefore, the correct equation that represents this scenario is:
C. [tex]\( 12 = \frac{45 + 9x}{x} \)[/tex]
