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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

Respuesta :

sqdancefan

Answer:

   (E)  450

Step-by-step 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.

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