ACT Math · Ratios, rates, and percents

A recipe for 8 servings uses 2 cups of sugar. How much sugar is needed for 20 servings, at the same rate?

A recipe for 8 servings uses 2 cups of sugar. How much sugar is needed for 20 servings, at the same rate?

Answer and explanation

Answer: B: 5 cups

The rate is constant, so use a proportion: 28=x20\frac{2}{8}=\frac{x}{20}. Cross-multiply: 8x=408x=40, so x=5x=5 cups, choice B. As a unit rate, each serving needs 28=0.25\frac{2}{8}=0.25 cup, and 20(0.25)=520(0.25)=5. Choice A (44) scales by 22 instead of 2.52.5, which would be right for 1616 servings. Choice C (66) scales by 33. Choice D (88) is the number of servings in the original recipe, not an amount of sugar. Since 2020 is 2.52.5 times 88, the sugar must be 2.52.5 times 22.

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