Answer :
To solve this problem, let's break it down step by step.
1. Understand the Components:
- Justine pays a one-time registration fee of \[tex]$45.
- She also pays \$[/tex]9 per lesson.
- The average cost per lesson, including the registration fee, is \[tex]$12.
- She has taken \(x\) lessons.
2. Calculate the Total Cost:
- Total cost = Registration fee + (Number of lessons × Cost per lesson)
- Total cost = \$[/tex]45 + [tex]\(x \times 9\)[/tex]
3. Average Cost per Lesson:
- Given that the average cost per lesson is \[tex]$12, we can express this as:
- Average cost per lesson = Total cost / Number of lessons
- Substitute the known expression for total cost: \(12 = (\$[/tex]45 + 9x) / x\)
4. Simplify the Equation:
- Start with the equation: [tex]\(12 = (45 + 9x) / x\)[/tex]
- Multiply both sides by [tex]\(x\)[/tex] to eliminate the fraction: [tex]\(12x = 45 + 9x\)[/tex]
- Rearrange the equation:
- Subtract [tex]\(9x\)[/tex] from both sides: [tex]\(12x - 9x = 45\)[/tex]
- Simplify: [tex]\(3x = 45\)[/tex]
Since none of the options A, B, C, or D match this derived equation, let's examine the options to see if any simplified or alternative form might reflect this scenario correctly:
- Option C resembles a structure with division, [tex]\(12 = \frac{5+k}{x}\)[/tex], suggesting it intends a similar form, but it doesn't convert directly to the cost pattern needed.
Therefore, after reviewing the steps, none of the provided options accurately represent the derived relationship. It's possible that the options have been misinterpreted or formatted in a way that doesn't directly reflect the scenario provided.
If you need any further explanations or have other questions, feel free to ask!
1. Understand the Components:
- Justine pays a one-time registration fee of \[tex]$45.
- She also pays \$[/tex]9 per lesson.
- The average cost per lesson, including the registration fee, is \[tex]$12.
- She has taken \(x\) lessons.
2. Calculate the Total Cost:
- Total cost = Registration fee + (Number of lessons × Cost per lesson)
- Total cost = \$[/tex]45 + [tex]\(x \times 9\)[/tex]
3. Average Cost per Lesson:
- Given that the average cost per lesson is \[tex]$12, we can express this as:
- Average cost per lesson = Total cost / Number of lessons
- Substitute the known expression for total cost: \(12 = (\$[/tex]45 + 9x) / x\)
4. Simplify the Equation:
- Start with the equation: [tex]\(12 = (45 + 9x) / x\)[/tex]
- Multiply both sides by [tex]\(x\)[/tex] to eliminate the fraction: [tex]\(12x = 45 + 9x\)[/tex]
- Rearrange the equation:
- Subtract [tex]\(9x\)[/tex] from both sides: [tex]\(12x - 9x = 45\)[/tex]
- Simplify: [tex]\(3x = 45\)[/tex]
Since none of the options A, B, C, or D match this derived equation, let's examine the options to see if any simplified or alternative form might reflect this scenario correctly:
- Option C resembles a structure with division, [tex]\(12 = \frac{5+k}{x}\)[/tex], suggesting it intends a similar form, but it doesn't convert directly to the cost pattern needed.
Therefore, after reviewing the steps, none of the provided options accurately represent the derived relationship. It's possible that the options have been misinterpreted or formatted in a way that doesn't directly reflect the scenario provided.
If you need any further explanations or have other questions, feel free to ask!
