If ¾ quart of lemonade concentrate is mixed with 6 ⅔ quarts of water to make lemonade for 40 people, how many quarts of lemonade concentrate are needed to make the lemonade for 24 people?
Correct answer: A. 9/20
- A. 9/20
- B. 7/20
- C. 2/5
- D. 3/10
Explanation
To solve this problem, we need to set up a proportion based on the original mixture for 40 people. We have ¾ quart of concentrate for 40 people. We want to find out how much concentrate is needed for 24 people.Set up the proportion: (¾ quart / 40 people) = (x quart / 24 people).By cross-multiplying, we get: 40x = 24 × ¾. Simplifying this gives x = 18/40 = 9/20.Therefore, 9/20 quarts of concentrate are needed for 24 people. This maintains the same ratio of concentrate to people as the original mixture.The other options are incorrect because they do not maintain the correct proportion based on the original recipe.
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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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