Question

Write a system of equations to describe the situation below, solve using any method, and Fill in the blanks.

Natalie is a salon owner. Yesterday, she did 3 haircuts and colored the hair of 1 client,
charging a total of $239. Today, she did 2 haircuts and colored the hair of 1 client, charging a
total of $192. How much does Natalie charge for her services?


Natalie charges $___
for a haircut and $__
for a coloring

Answer 1

1 haircut = 47 dollars

1 colouring = 98 dollars

Explanation:

Let
`x` be equal to the cost of 1 haircut.

Let
`y` be equal to the cost of 1 colouring treatment.

1) Form equations

Equation 1: 3 haircuts + 1 colour = 239 dollars

⇒
`3x+y=239`

Equation 2: 2 haircuts + 1 colour = 192 dollars

⇒
`2x+y=192`

2) Solve the system of equations

Subtract equation 2 from equation 1 to cancel out y (elimination)

-
`3x+y=239\\2x+y=192`

⇒
`3x-2x+y-y=239-192\\x=47`

Therefore, Natalie charges 47 dollars for 1 haircut.

Plug x back into one of the equations to solve for y

`2(47)+y=192\\94+y=192`

Subtract both sides by 94

`94+y-94=192-94\\y=98`

Therefore, Natalie charges 98 dollars for 1 colouring treatment.

I hope this helps!