Question

Akira is a salon owner. Yesterday, she did 2 haircuts and colored the hair of 1 client, charging a total of $194. Today, she did 2 haircuts and colored the hair of 4 clients, charging a total of $494. How much does Akira charge for her services?

Answer 1

Answer:

$\boxed {\boxed {\sf Haircut: \ 47 \ and \ Color: \ 100}}$

Step-by-step explanation:

Let's set up a system of equations. (1 equation for yesterday and 1 for today).

• Let h = haircut and c= color

$2h+1c= 194$  (Yesterday: 2 haircuts and 1 color for $194).

$2h+4c= 494$ (Today: 2 haircuts and 4 colors for $494).

Notice that both equations have a 2h. If we subtract the two equations, the 2h will cancel and leave us with one variable, c.

$\ \ (2h+1c=194) \\- (2h+4c=494)$

$\ \ 1c=194 \\- (4c=494)$

$-3c= -300$

Since we are solving for c, we must isolate the variable. It is being multiplied by -3. The inverse of multiplication is division. Divide both sides by -3.

$-3c/-3=-300/-3 \\c= -300/-3 \\c=100$

Now we have to solve for h. Plug 100 in for c in the first equation.

$2h+1(100)= 194 \\2h+100=194$

100 is being added, so we must subtract 100 from both sides.

$2h+100=194-100 \\2h=94$

h is being multiplied by 2, so we divide both sides by 2.

$2h/2=94 \\h=47$

A haircut costs $47 and a color costs $100.