Question

Solution Y is 40 percent sugar by volume, and solution X is 20 percent sugar by volume. How many gallons of solution X must be added to 150 gallons of solution Y to create a solution that is 25 percent sugar by volume?

A) 37.5
(B) 75
(C) 150
(D) 240
(E) 450

Answer 1

(E) 450

Explanation:

Let x represent the number of gallons of solution X that must be added to the mix. Then the amount of sugar in the mix is ...

0.20x +0.40·150 = 0.25(150 +x)

0.20x +60 = 37.5 +0.25x . . . eliminate parentheses

22.5 + 0.20x = 0.25x . . . . . . subtract 37.5

22.5 = 0.05x . . . . . . . . . . . . . subtract 0.20x

450 = x . . . . . . . . . . . . . . . . . . multiply by 20

450 gallons of solution X must be added to make a 25% sugar solution.