Question

Vivian is going to hire a makeup artist for a fashion show and is comparing prices. Carla charges $60 as a booking fee and an additional $81 per hour. Wanda charges $79 per hour, plus a booking fee of $64. Depending on the length of the show, the cost could end up being the same for either artist. How long would the show be? What would the cost be?

A. 3 hours, $303
B. 4 hours, $364
C. 5 hours, $405
D. 6 hours, $446

Answer 1

The show would be 2 hours long and cost $222.

Step-by-step explanation:

To determine how long the show would be and the cost, we need to find the point at which the costs for Carla and Wanda would be the same. Let's represent the number of hours as x:

For Carla, the cost would be $60 (booking fee) + $81x (hourly rate), so the cost function for Carla is C(x) = 60 + 81x.

For Wanda, the cost would be $79x (hourly rate) + $64 (booking fee), so the cost function for Wanda is C(x) = 79x + 64.

To find the point at which the costs are equal, we set the two cost functions equal to each other:

60 + 81x = 79x + 64

Simplifying the equation, we get:

2x = 4

x = 2

The show would be 2 hours long. To find the cost, we substitute this value into either of the cost functions:

C(2) = 60 + 81(2) = 60 + 162 = $222.

Therefore, the correct answer is B. 2 hours, $222.