Justine enrolls in a music program. The cost of the program includes a one-time registration fee of [tex] \$45 [/tex] and a fee of [tex] \$9 [/tex] per lesson. If the average cost per music lesson is [tex] \$12 [/tex] and Justine has taken [tex] x [/tex] classes, which equation represents this scenario?

A. [tex] 12 = \frac{54}{2} [/tex]

B. [tex] 12 = 45 + \frac{2}{2} [/tex]

C. [tex] 12 = \frac{45 + 92}{z} [/tex]

D. [tex] 12 = \frac{45 + 9x}{x} [/tex]

To solve this problem, we need to determine which equation correctly represents the scenario where Justine enrolls in a music program with a one-time registration fee and a per-lesson fee. Let's go through the problem details step-by-step:

1. Understanding the Costs:
- Registration Fee: \[tex]$45 (one-time)
- Cost Per Lesson: \$[/tex]9

2. Average Cost Per Lesson:
- We are given that the average cost per lesson is \[tex]$12.

3. Formulating the Equation:
- The total cost for taking $ z $ lessons would be the sum of the registration fee and the cost for $ z $ lessons:
\[
\text{Total Cost} = 45 + 9z
\]
- To find the average cost per lesson, we divide the total cost by the number of lessons $ z $:
\[
\text{Average Cost per Lesson} = \frac{45 + 9z}{z}
\]
- We know this average should be equal to \$[/tex]12, so we set up the equation:
[tex]\[
\frac{45 + 9z}{z} = 12
\][/tex]

4. Solving the Equation:
- Multiply both sides by [tex]$ z $[/tex] to eliminate the fraction:
[tex]\[
45 + 9z = 12z
\][/tex]
- Rearrange the equation to solve for [tex]$ z $[/tex]:
[tex]\[
12z - 9z = 45
\][/tex]
[tex]\[
3z = 45
\][/tex]
- Divide by 3:
[tex]\[
z = 15
\][/tex]

From our work, it's clear that the correct equation representing the scenario is [tex]$ 12 = \frac{45 + 9z}{z} $[/tex], which matches option D:

D. [tex]$ 12 = \frac{45 + 9z}{z} $[/tex]

So, the right choice is D.