If 2a = 7b and 14b = c, then a is equal to
Correct answer: D. c/4
- A. 4c
- B. 2c
- C. c
- D. c/4
Explanation
To solve the given problem, start by substituting the second equation into the first. We have 2a = 7b and 14b = c. From 14b = c, we can express b as b = c/14. Substitute this into the first equation: 2a = 7(c/14). Simplifying, we obtain 2a = c/2. Divide both sides by 2, resulting in a = c/4. Therefore, the correct answer is c/4.Option A: 4c assumes that a is multiplied by c in a way that does not align with the given equations. Option B: 2c suggests an incorrect direct proportion between a and c. Option C: c implies that a equals c without considering the necessary division. Only Option D correctly reflects the relationships and divisions needed according to the given expressions.
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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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