Question

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?

Answer 1

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! :)