guerrero25 wrote:

One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?

A. 34%

B. 24%

C. 22%

D. 18%

E. 8.5%

Let’s let x = the amount of solution, which initially contains 10% sugar. We remove one-fourth of that solution (.25x), which has 10% sugar. Then we replace that .25x with a solution of unknown percentage (p) of sugar. These actions result in our still having x amount of solution, but now with 16% sugar. We can summarize this in the following equation:

x(0.10) - (0.25x)(0.10) + (0.25x)(p) = x(0.16)

0.10x - 0.025x + 0.25xp = 0.16x

100x - 25x + 250xp = 160x

250xp = 85x

p = 85/250 = .34

Thus, the second solution was 34% sugar by weight.

Answer: A

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