The LHS is the amount of salt in the initial solution, minus the amount of water evaporated. Does that sound right?
The RHS is the amount of salt in the target solution.
What has to be changed?
The right side must be changed.
20(0.20) - w = 0.30(20 + w)
Why? Now you're adding water.
Please explain the meaning of each side -- and especially why you would subtract an amount of water from an amount of salt.
Correct (up to a point).20(0.20) = 0.30(20 - w)
w = 6.7
I would use the fact that the amount of salt will remain constant, so we can equate the amount of salt before and after evaporation (of \(w\) ounces of water):
[MATH]0.2(20)=0.3(20-w)[/MATH]
[MATH]40=60-3w[/MATH]
[MATH]3w=20[/MATH]
[MATH]w=\frac{20}{3}[/MATH]
I would use the exact amount here rather than rounding.
I say the answer is 7 ounces of water should be evaporated to make a 30% solution.
The new solution will be 7 ounces less, namely 13 ounces; 30% of that, 0.30*13 = 3.9 ounces, is supposed to be salt, compared to 0.20*20 = 4 ounces of salt that you actually have. The actual concentration would be 4/13 = 30.77%. So you didn't quite accomplish the goal.Rita has 20 ounces of a 20% of salt solution. How much water should she evaporate to make it a 30% solution?
Good, as far as the words are concerned. But I see no reason to round the answer so much, so I'd actually call this answer wrong if I were grading it.
One more comment, to complete the task: I find it helpful (especially in learning) to check that final answer (in words) against the original problem.
The new solution will be 7 ounces less, namely 13 ounces; 30% of that, 0.30*13 = 3.9 ounces, is supposed to be salt, compared to 0.20*20 = 4 ounces of salt that you actually have. The actual concentration would be 4/13 = 30.77%. So you didn't quite accomplish the goal.
If you had not rounded, and said 6 2/3 ounces, then we'd have 20 - 6 2/3 = 13 1/3 ounces, 30% of which is 4 ounces of salt, so it works out exactly. If you used your previous rounded answer of 6.7, you'd have 13.3 ounces, of which 3.99 ounces should be salt, and the actual concentration would be 4/13.3 = 30.075%, which is probably good enough (depending on context).