Question

To make a specific hair dye, a hair stylist uses a ratio of 9/8 oz of red tone, 3/4 oz of gray tone, and 5/8 oz of brown tone if the stylist needs 20oz of dye how much of each dye color is needed

Answer 1

`9\ oz` ---> red tone

`6\ oz` ----> gray tone

`5\ oz` -----> brown tone

Explanation:

Let

x-----> the number of ounces of red tone

y----> the number of ounces of gray tone

z---> the number of ounces of brown tone

we know that

`x+y+z=20` -----> equation A

`(x)/(y)=((9/8))/((3/4))=1.5`

`x=1.5y` -----> equation B

`(x)/(z)=((9/8))/((5/8))=1.8`

`x=1.8z` -----> equation C

`(y)/(z)=((3/4))/((5/8))=1.2`

`y=1.2z` -----> equation D

substitute equation D and equation equation C in equation A

`1.8z+1.2z+z=20`

solve for z

`4z=20`

`z=5\ oz` -----> brown tone

Find the value of x

`x=1.8z` ----->
`x=1.8(5)=9\ oz` ---> red tone

Find the value of y

`y=1.2z`--->
`y=1.2(5)=6\ oz` ----> gray tone