Question

To make a specific hair dye a hairstylist uses a ratio of one and 1/8 oz of red tone 3/4 oz of Gray tone and 5/8 oz of Brown tone if the stylist needs to make 20 oz of dye how much of each dye color is needed?

Answer 1

Answer: To make 20 oz of hair dye, the hairstylist needs to use 1 and 1/8 oz of red tone, 3/4 oz of gray tone and 5/8 oz of brown tone.

We can use proportionality to figure out how much of each dye color is needed.

Let's call the amount of red dye needed x, the amount of gray dye needed y and the amount of brown dye needed z.

According to the proportionality, we can write the following equation:

(1 + 1/8)x + (3/4)y + (5/8)z = 20

To find the amount of each dye color needed, we can solve this equation for x, y and z.

First, we can clear the fractions by multiplying all terms by 8:

(8 + 1)x + (6)y + (5)z = 160

Now we can solve for x:

9x + 6y + 5z = 160

x = (160 - 6y - 5z)/9

Similarly, we can solve for y and z:

y = (160 - 9x - 5z)/6

z = (160 - 9x - 6y)/5

Now we can substitute the desired amount of 20 oz into the equation and solve for x, y and z

Explanation: