Question

Vivian is a salon owner. Yesterday she did 2 haircuts and colored the hair of 4 clients, charging a total of $422. Today, she did 5 haircuts and colored the hair of 4 clients, charging a total $573. How much does Vivian charge for her services?

Answer 1

Answer:

Haircuts cost $50.33

Hair Color costs $80.33

Step-by-step explanation:

Let haircut be cost "a"

coloring be cost "b"

2 haircut, 4 coloring equals 422, we can write:

2a + 4b = 422 {Equation 1}

5 haircut, 4 coloring, equals 573, we can write:

5a + 4b = 573 {Equation 2}

We now multiply equation 1 with -1 and add it with Equation 2 to get:

-1(2a + 4b = 422) = -2a - 4b = -422

Now,

-2a - 4b = -422

5a + 4b = 573

----------------------

3a = 151

a = 151/3 = $50.33

Now, to find b, we plug in this value into any equation and solve for b:

2a + 4b = 422

2(50.33) + 4b = 422

4b = 422 - 100.66

b = $80.33

Haircuts cost $50.33

Hair Color costs $80.33