MATH SOLVE

4 months ago

Q:
# Tracy is a salon owner. Yesterday, she did 1 haircut and colored the hair of 2 clients, charging a total of $191. Today, she did 5 haircuts and colored the hair of 2 clients, charging a total of $355. How much does Tracy charge for her services?

Accepted Solution

A:

x= $ cost of haircut

y= $ cost of hair coloring

Yesterday's Equation

1x + 2y= $191

Today's Equation

5x + 2y= $355

Solve for one variable in either equation and substitute in other equation

x + 2y= $191

subtract 2y from both sides

x= 191 - 2y

Substitute x value in today's equation

5x + 2y= $355

5(191 - 2y) + 2y= 355

multiply 5 by all in parentheses

(5*191) + (5*-2y) + 2y= 355

955 - 10y + 2y= 355

955 - 8y= 355

subtract 955 from both sides

-8y= -600

divide both sides by -8

y= $75 cost of hair coloring

Substitute y value to find x value

1x + 2y= $191

x + 2(75)= 191

x + 150= 191

subtract 150 from both sides

x= $41 cost of haircut

ANSWER: She charges $41 for a haircut and $75 for hair coloring.

Hope this helps! :)

y= $ cost of hair coloring

Yesterday's Equation

1x + 2y= $191

Today's Equation

5x + 2y= $355

Solve for one variable in either equation and substitute in other equation

x + 2y= $191

subtract 2y from both sides

x= 191 - 2y

Substitute x value in today's equation

5x + 2y= $355

5(191 - 2y) + 2y= 355

multiply 5 by all in parentheses

(5*191) + (5*-2y) + 2y= 355

955 - 10y + 2y= 355

955 - 8y= 355

subtract 955 from both sides

-8y= -600

divide both sides by -8

y= $75 cost of hair coloring

Substitute y value to find x value

1x + 2y= $191

x + 2(75)= 191

x + 150= 191

subtract 150 from both sides

x= $41 cost of haircut

ANSWER: She charges $41 for a haircut and $75 for hair coloring.

Hope this helps! :)