Question

Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks. Sally is a hairdresser. Before her lunch break, she gave 1 haircut and colored the hair of 3 clients in 199 minutes. After lunch, she colored the hair of 1 client in 61 minutes. How long does it take for Sally to perform each type of service, assuming the amount of time doesn't vary from client to client?

a) Haircut: 80 minutes, Coloring: 13 minutes
b) Haircut: 61 minutes, Coloring: 13 minutes
c) Haircut: 90 minutes, Coloring: 45 minutes
d) Haircut: 199 minutes, Coloring: 61 minutes

Answer 1

After setting up a system of equations with variables representing the times for haircuts and colorings, it was found that a haircut takes 16 minutes and coloring takes 61 minutes. However, these times do not match any of the provided options, suggesting a mistake in the problem or its options.

Step-by-step explanation:

To solve Sally's service times for haircuts and hair coloring, we need to set up a system of equations based on the information given:

• Before lunch: 1 haircut + 3 colorings = 199 minutes
• After lunch: 1 coloring = 61 minutes

Let h represent the time it takes Sally to give a haircut and c represent the time it takes to color hair. Now, we can write the following system of equations:

1. h + 3c = 199
2. c = 61

Using the second equation, we know that coloring time, c, is 61 minutes. This can be substituted into the first equation to find the haircut time, h:

1. h + 3(61) = 199
2. h + 183 = 199
3. h = 199 - 183
4. h = 16 minutes

However, the option of 16 minutes for a haircut and 61 minutes for coloring is not listed in the question, indicating a possible error either in the calculations or in the provided options. Given that none of the presented options match the solved times, there might be a mistake in the question or the student may need to check the information again.