A 32-acre field yields 768 bushels of corn each year. How many more acres are needed to yield 960 bushels of corn each year?
Correct answer: B. 8
- A. 6
- B. 8
- C. 10
- D. 12
Explanation
To determine the additional acres required, set up a proportion based on the initial data: a 32-acre field yields 768 bushels. Express this as a ratio: 32 acres/768 bushels = (32 + x) acres/960 bushels, where 'x' is the number of additional acres needed.Cross-multiply to obtain: 32 * 960 = (32 + x) * 768.Upon solving, you get 30,720 = 24,576 + 768x.Further simplification gives 6,144 = 768x, leading to x = 8.Therefore, 8 more acres are required to reach the desired yield of 960 bushels. Other options either underestimate or overestimate the necessary acres based on incorrect calculations of the proportion.
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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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