Word Problems 2!?

Question

Several of you wondered why I was making these problems on up. It is an assigment I have--to be able to create these problems, to show that I fully understand how they work (not just solving them) and see if others find them workable.

-The ratio of the numerator to the denominator of a certain fraction is five to eight. If five is subtracted from the numerator and four is added to the denominator, the new fraction reduces to one-half. Find the originial fraction.

-A mixture contains five quarts of acid and water, and forty percent is acid. If the mixture is to be weakened to thirty perfect, how much water must be added? ___quarts of water must be added. (Answer should be in fraction form)

I think I'll throw in an age problem too, hehe.
-A girl is now one-fourth as old as her father, and in seven years she will be one-half as old as her father was twelve years ago. Find their present ages!

Answer 1

13 girl
52 father

Answer 2

n/d = 5/8 5d = 8n d = 8n/5

n -5 /d + 4 = 1/2 d + 4 = 2(n-5) d + 4 = 2n - 10

....................................................d = 2n - 14
...............................................8n/5 = 2n - 14

8n = 10n - 70 n = 35 d = 56 35/56 = 5/8


g = 1/4 f g+7 = 1/2 (f+7) g = 1/2 f +7/2 - 7

.............................................g = 1/2 f - 7/2

1/4 f = 1/2 f - 7/2

-1/4 f = -7/2

f =14 g = 7 - 7/2 = 3 1/2