chaitanya.bhansali wrote: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?
1.) 37.5
2.) 50
3) 62.5
4) 300
5) 450
Since Y is 40% sugar, the amount of sugar in 150 gallons of Y = 40% of 150 = 60 gallons.
An alternate approach is to PLUG IN THE ANSWERS, which represent the amount of X that must be added.
When the correct answer is plugged in, sugar/total = 25% = 1/4.
Answer choice D: 300 gallons
Since X is 20% sugar, the amount of sugar in 300 gallons of X = 20% of 300 = 60 gallons.
(sugar in X + sugar in Y)/(total X + total Y) = (60+60)/(300+150) = 120/450 = 4/15.
Since 4/15 is greater than 1/4, the proportion of sugar must DECREASE.
X has a lower sugar percentage than does Y.
Thus, to decrease the percentage of sugar in the resulting mixture, MORE X must be added.
The correct answer is
E.
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