Find Amount of Water

harpazo

harpazo

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Rita has 20 ounces of a 20% of salt solution. How much water should she evaporate to make it a 30% solution?

Solution:

Let w = amount of water that Rita should evaporate to make a 30% solution.

20(0.20) - w = 0.30(20 - w)

Correct set up?
 
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?
 
Dr.Peterson said:
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?
Click to expand...

The right side must be changed.

20(0.20) - w = 0.30(20 + w)
 
harpazo said:
The right side must be changed.

20(0.20) - w = 0.30(20 + w)
Click to expand...

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.
 
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.
 
harpazo said:
20(0.20) = 0.30(20 - w)

w = 6.7
Click to expand...
Correct (up to a point).

But don't forget to answer the question: It doesn't ask what w is (you invented the variable); it asks "How much water should she evaporate?" That requires, among other things, a unit, since 6.7 (actually 6 2/3) is not an amount, just a number. This is part of the reason we define variables including the units.
 
MarkFL said:
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.
Click to expand...

I say the answer is 7 ounces of water should be evaporated to make a 30% solution.
 
harpazo said:
I say the answer is 7 ounces of water should be evaporated to make a 30% solution.
Click to expand...

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.
harpazo said:
Rita has 20 ounces of a 20% of salt solution. How much water should she evaporate to make it a 30% solution?
Click to expand...
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).
 
Dr.Peterson said:
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).
Click to expand...

I thank you for your input and reply.
 
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