Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad dressing. If Larry has 8 cups of oil, 7 cups of vinegar, and access to any amount of water, what is the maximum number of cups of salad dressing he can make with the ingredients he has available, if fractional cup measurements are possible?

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Official Explanation

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We can create the ratio of oil : vinegar : water =

3x : 2x : x

Since Larry has 8 cups of oil, we have:

3x = 8

→

x = \frac{8}{3} = 2\frac{2}{3}

Since Larry has 7 cups of vinegar, we have:

2x = 7

→

x = \frac{7}{2} = 3.5

We see that we must use the smaller of the two values of x since, if we used 3.5 for x, we would need to have

3 \times 3.5 = 10.5

cups of oil (but we have only 8 cups of oil).…

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What this question tests

Your ability to convert between fractions, ratios, and decimals and to reason proportionally.

Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.