Hi rvc27,
In these types of mixture questions, if the answers are numbers, then it's likely that you can TEST THE ANSWERS to quickly get to the solution. Here's how:
First, we need to know about the original mixture of vinegar and water. We're told that a 5 gallon mixture is 8% vinegar....
(5 gallons)(.08) = 0.4 gallons vinegar
The rest = 4.6 gallons water
We're told to ADD WATER until the mixture goes from 8% vinegar to 4% vinegar.
Since the answer choices are numbers, we know that one of them will lead us to a 4% mix when added to the current mix. Changing 8% to 4% means that we have to add a significant amount of water (relative to what we started with), so I would TEST one of the bigger numbers first.
Let's TEST B
If 5 gallons of water were added, then we'd have....
0.4 gallons vinegar
9.6 gallons of water
0.4/10 = 4% vinegar. This is EXACTLY what we're looking for, so B MUST be the answer.
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