Question

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

Answer 1

Answer:

1 haircut = 47 dollars

1 colouring = 98 dollars

Step-by-step 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!