Question

To make a specific hair dye, a hair stylist uses a ratio of 1 1/8 ounces of red tone, 3/4 ounces of gray tone, and 5/8 ounces of brown tone. If the stylist needs to make 20 ounces of dye, how much of each dye color is needed? If the stylist needs to make 100 ounces of dye, how much of each dye color is needed? ( you do not need to do question 5 or letter e

Answer 1

Answer: To make 20 ounces of dye, we need 3 oz red tone, 6 oz of gray tone and 5 oz of brown tone.

To make 100 ounces of dye, we need 15 oz red tone, 30 oz of gray tone and 25 oz of brown tone.

Explanation:

The amount of specific hair dye made by given ingredients=
`1(1)/(8)+(3)/(4)+(5)/(8)`

`=(9)/(8)+(3)/(4)+(5)/(8)`

`=(9+6+5)/(8)=(20)/(8)=(5)/(2)\ oz`

Therefore , The amount of specific hair dye made by given ingredients=
`(5)/(2)` qz

Multiply reciprocal of
`(5)/(2)` to each ingredient to find the amount of each ingredient required to make 1 oz of specific hair dye.

To make 1 oz of specific dye, the amount of red tone needed
`=(3)/(8)*(2)/(5)=(3)/(20)\ oz`

Similarly, Gray tone=
`(3)/(4)*(2)/(5)=(3)/(10)\ oz`

Brown tone=
`(5)/(8)*(2)/(5)=(1)/(4)\ oz`

Now, multiply 20, to each

To make 20 oz of specific dye, the amount of red tone needed
`=(3)/(20)*20=3\ oz`

Similarly, Gray tone=
`(3)/(10)*20=6\ oz`

Brown tone=
`(1)/(4)*20=5\ oz`

To find each dye to make 100 ounces of dye, multiply 5 to the above amounts, [since
`100=20*5` ]

To make 20 oz of specific dye, the amount of red tone needed
`=15\ oz`

Similarly, Gray tone=
`30\ oz`

Brown tone=
`25\ oz`

Answer 2

Hi!

The answers are:

a. For 20oz.

• Red tone: 9oz.
• Grey tone: 6oz.
• Brown tone: 5oz.

b.For 100oz.

• Red tone: 45oz.
• Grey tone: 30oz.
• Brown tone: 25oz.

Explanation:

First, you have to find the total ounces it use for the specific hair dye.

`1 (1)/(8)oz + (3)/(4)oz + (5)/(8)oz = 2,5oz`

A) Now, because the ratio is always the same, you can use Rule of three to know how much uses to prepare 20 ounces.

2,5 oz specific hair dye → 1 1/8 oz red tone.

20 oz → x oz red tone. //multiply 20 by 1 1/8 and divide by 2,5

`x = (20oz \cdot 1 (1)/(8)oz)/(2,5oz) = 9oz`

2,5 oz specific hair dye → 3/4 oz gray tone.

20 oz → x oz gray tone. //multiply 20 by 3/4 and divide by 2,5

`x = (20oz \cdot (3)/(4)oz)/(2,5oz) = 6oz`

2,5 oz specific hair dye → 5/8 oz brown tone.

20 oz → x oz brown tone. //multiply 20 by 5/8 and divide by 2,5

`x = (20oz \cdot (5)/(8)oz)/(2,5oz) = 5oz`

b) Now, to prepare 100 ounces because the ratio is still the same, you can multiply 5 times the ounces that you had obtained in a).

• 5*9oz = 45oz red tone.

• 5*6oz = 30oz gray tone.

• 5*5oz = 25oz brown tone.

• 100oz total used.