propotions question

neeg wrote:How many liters of water must be evaporated from 50 litres of a 3 percent sugar solution to get a 5 percent solution?

Ans choices
(A)2 (B)4 (C)6 (D)10 (E)20

If the 50-liter solution is 3% sugar, then there are 1.5 litres of sugar in the solution (since 3% of 50 is 1.5)

Let x be the number of liters that are evaporated.

This means the new volume is 50-x liters, but the amount of sugar remains at 1.5 liters (since no sugar leaves the solution)

We want a 5% solution. In other words 5% of the 50-x liters must be sugar.
In other words 5% of 50-x liters of solution equals 1.5 liters of sugar.
Or . . . (5/100)(50-x) = 1.5 [solve for x]
Multiply both sides by 100 to get: 5(50-x) = 150
Expand: 250 - 5x = 150
Rearrange: 100 = 5x
Solve: 20 = x

Answer: E

Cheers,
Brent