Five gallons of a solution of vinegar and water with 8% vinegar is to be diluted with water to make a 4% vinegar mixture. How many gallons of water should be added?
Choices.
A) 10  B) 5  C) 4  D) 2  E) 1
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.   Final Answer:   5
<result>B</result>
Five gallons of a solution of vinegar and water with 8% vinegar is to be diluted with water to make a 4% vinegar mixture. How many gallons of water should be added?