Hi,
I was working on this problem from Manhattan GRE Word problem book. The 2nd problem in Page 121. And I can't seem to understand a certain portion of the problem.
A Salad dressing requires oil, vinegar and water in the ratio of 2:1:3. If Oliver has 1 cup of oil, 1/3 cup of vinegar and 2 cups of water, what is the maximum number of cups of dressing that he can mix?
Solution from the book : 2 cups.
Explanation from the book :
Try the limits. If Oliver used 1 cup of oil, his recipe would require 1/2 cup of vinegar and 1 1/2 cups of water. He does not have enough vinegar. If he used 1/3 cup of vinegar, he would need 2/3 cups of oil and 1 cup of water, both of which he has. He would then have 2/3 + 1/3 + 1 = 2 cups of dressing. He cannot possible make more dressing than this because he does not have any more vinegar.
I don't understand how they calculate the ratios. Meaning if Oliver decided to use 1 cup of oil, how do we determine that he needs 1/2 cup of vinegar and 1 1/2 cups of water and so forth. I know we have to use the given ratio 2:1:3 to arrive at this but I'm not able to correlate to get the solution. Please help me understand.
Thanks.