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Sagot :
7 gallons of 76% solution contain 0.76×(7 gal) = 5.32 gal of sugar
10 gal of c% solution (c for concentration) contain c/100×(10 gal) = c/10 gal of sugar
(for example, if you have 10 gal of 50% solution, then it contains 50/10 = 5 gal of sugar)
Mixing the two gives a new solution with a total volume of 17 gal. If its concentration ends up at 64%, then it must contain 0.64×(17 gal) = 10.88 gal of sugar. This means
(sugar in 76% solution) + (sugar in c% solution) = 10.88 gal
5.32 gal + c/10 gal = 10.88 gal
c/10 gal = 5.56 gal
c = 50.56 ≈ 51
which makes the answer A.
Answer:
d. 56
Equation:
Let x = the percent of the 10 gallon sugar solution
10x + 76(7) = 64(10 + 7)
10x + 532 = 1088
10x = 1088 - 532
10x/10 = 556/10
x = 55.6
55.6 is closest to 56, therefore, the answer is 56%
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