A paint that contains 26 % green dye is mixed with a paint that contains 16 % green dye. How many gallons of each must be used to make 90 gal of paint that is 22 % green dye?

Number of gallons for paint 1 = 54

Number of gallons for paint 2 = 36

Step-by-step explanation:

Let the amount of gallons for paint 1 = x

amount of gallons for paint 2 = y

Total gallons = 90

So, x + y = 90 ... Equation 1

26% green dye for paint 1 = 0.26*x = 0.26x

16% green dye for paint 2 = 0.16*y = 0.16y

22% green dye for the mixture = 0.22*90 = 19.8

So, 0.26x + 0.16y = 19.8 ... Equation 2

The system of equations is thus

x + y = 90 ... Equation 1

0.26x + 0.16y = 19.8 ... Equation 2

Multiply equation 1 by 0.26

0.26x + 0.26y = 90*0.26 = 23.4 ... Equation 3

We then have,

0.26x + 0.16y = 19.8 ... Equation 2

0.26x + 0.26y = 23.4 ... Equation 3

Subtract equation 2 from equation 3

0.26x - 0.26x + 0.26y - 0.16y = 23.4 - 19.8

0.10y = 3.6

Divide both sides by 0.10

0.10y/0.10 = 3.6/0.10

y = 36 gallons

Use y = 36 in equation 1

x + 36 = 90

x = 90 - 36

x = 54 gallons

54 gallons of 26% green dye and 54 gallons of 16% green dye

Step-by-step explanation:

Let x be the quantity of gallons needed to mix both paints.

The equation will be:

0.26x + 0.16 (90gal - x) = 0.22 (90gal)

0.26x + 14.4 - 0.16x = 19.8

Making x subject of formular

0.26x - 0.16x = 19.8 - 14.4

0.1x = 5.4

X = 5.4/0.1 = 54 gallons