Experiencing a brain freeze here. There are two related word problems in the book I am reading. The first one I solved, the second one is giving me fits. The first problem reads:
How much water must be evaporated from 500 grams of a 10% salt solution in order to obtain a solution containing 15% salt?
My solution was to make x represent the amount of water to be evaporated. My equation was:
90% (500) - x = 85% (500 - x)
Solving: 450 - x = 425 - .85x
25 = .15x
x = 166 2/3 grams
which is correct.
The second question states:
Generalize Exercise 57 as follows: Let a, b, and d be positive real numbers with a < b < 100. Given a solution of d grams of salt water that is a% salt, how much water must be evaporated in order that the resulting mixture will be b% salt? Express the answer in terms of a, b, and d.
Here I've tried expressing the equation as
ad - x = b(d-x)
ad - x = bd -bx
ad - bd = x - bx
d(a - b) = x (1 - b)
(d(a - b))/(1 - b) = x
However, this gives an incorrect answer with the original numbers. The solution given in the book is
x = (d(b - a))/b
I can't for the life of me figure out how they got to this equation. Please help!