Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

Anna is going to hire a makeup artist for a fashion show and is comparing prices. Dylan charges $58 as a booking fee and an additional $63 per hour. Lexi charges $65 per hour, plus a booking fee of $54. Depending on the length of the show, the cost could end up being the same for either artist. What would the cost be? How long would the show be?


The cost would always be $
 if the show lasted 
 hours.

To solve this problem, we'll create a system of equations to represent the total cost for each makeup artist and solve it using substitution.

### Step 1: Define variables
- Let $ x $ represent the number of hours the show lasts.
- Let $ C_D $ represent the total cost for Dylan.
- Let $ C_L $ represent the total cost for Lexi.

### Step 2: Create equations based on the information provided
- Dylan charges a booking fee of $58 and $63 per hour, so his total cost equation is:
  \[
  C_D = 58 + 63x
  \]
- Lexi charges a booking fee of $54 and $65 per hour, so her total cost equation is:
  \[
  C_L = 54 + 65x
  \]

### Step 3: Set up the equation where the costs are equal
To find when the cost is the same for both Dylan and Lexi, we set the two equations equal to each other:
\[
58 + 63x = 54 + 65x
\]

### Step 4: Solve the equation
Simplify and solve for $ x $:
\[
58 - 54 = 65x - 63x
\]
\[
4 = 2x
\]
\[
x = 2
\]

So, the show would last 2 hours.

### Step 5: Find the total cost
Substitute $ x = 2 $ into either cost equation (since the costs are the same):
\[
C_D = 58 + 63(2) = 58 + 126 = 184
\]
\[
C_L = 54 + 65(2) = 54 + 130 = 184
\]

### Final Answer:
The cost would always be **$184** if the show lasted **2 hours**.

---

Would you like more details or have any questions?

Here are 5 questions to expand on this:
1. What happens if the show lasts more than 2 hours? Which artist would be cheaper?
2. What is the cost difference if the show lasts 4 hours?
3. How would the equation change if Dylan offered a discount on his booking fee?
4. If Lexi increased her hourly rate to $70, how would that affect the solution?
5. How could you graph these equations to visualize the costs?

**Tip:** In cost comparison problems like this, setting the equations equal to each other helps identify the breakeven point.

Anna is going to hire a makeup artist for a fashion show and is comparing prices. Dylan charges $58 as a booking fee and an additional $63 per hour. Lexi charges $65 per hour, plus a booking fee of $54. Depending on the length of the show, the cost could end up being the same for either artist. What would the cost be? How long would the show be?

Discover how to compare the costs of two makeup artists for a fashion show using linear equations. Learn how Dylan's booking fee and hourly rate compare to Lexi's, and solve for when their costs are the same. This problem is suitable for students in Grades 8-10 and covers key concepts in algebra and cost comparison.

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