bmwhype2 wrote:

One fourth of a solution that was 10 percent 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%

How do I set this one up using the algebra?

Prolly more complicated than it needs to be, this one took me bout 15minutes =( I hate mixtures.

1/4x*1/10 --> 1/40x weight of sugar in the 1/4 mixture.

1/40x is replaced with something that yeilds 16/100x. 16/100x is the total weight of the sugar in x. Now to find the weight of the replacement we can take 3/40x (the amount that wasn't replaced, 3/40x is essentially 10% of 3/4x) and subtract it from the total.

16/100x -3/40x ---> 32/200x-15/200x ---> 17/200x equals weight of sugar in the new mixture.

We want weight of sugar over new mixture so 17/200x/1/4x the x's cancel and were left w/ 68/200 ---> .34

A