Question

Ten gallons of a sugar solution were mixed with 7 gallons of a 76 percent sugar solution to make a 64 percent sugar solution. Find the percent concentration of the first solution.

answers-
a. 51%
b. 60%
c. 48%
d. 56%

Answer 1

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 2

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%