Setting this problem up as a ratio of an amount divided by a total makes this really easy to solve. The question tells us that we have 2 ounces of real orange juice for every 100 ounces of drink. Thus, our juice-to-total ratio would look like this:

\(\frac{J}{T} = \frac{2}{100}\)

The problem then tells us that a particular bottle contains 32 ounces total. We can simply plug that 32-ounce amount into our total, \(T\), and solve for \(J\). Thus:

\(\frac{J}{32} = \frac{2}{100}\)

\(J = \frac{2*32}{100}=\frac{64}{100}\)

While we could further simplify 64/100 down to 16/25 or even to the decimal 0.64, the answers keep it fractional form, so we can stop there.

The answer is (E).Another way to solve this problem would be to look down at the answer choices and realize this problem might be a prime candidate for approximating. While all the answer choices are small, they are very different from each other, ranging from \(\frac{2}{100}\) to \(\frac{64}{100}\). The question tells us that there are only 2 ounces of juice in 100 ounces of drink. The "target" amount of drink (32 ounces) is approximately \(\frac{1}{3}\) of 100 ounces. Thus, the amount of juice should be about \(\frac{1}{3}\) of 2 ounces. \(\frac{1}{3}\) of 2 is \(\frac{2}{3}\), or about .67 ounces. The only answer choice that is even close to .67 is answer choice (E).

Any way you solve it, the answer is still (E).
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Aaron J. Pond

Veritas Prep Elite-Level Instructor

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