If a=3b, 4b=5c, 6c=7d, then what is \frac{d+a}{d-a} equal to?

  1. A. \frac{27}{43}
  2. B. \frac{43}{27}
  3. C. -\frac{27}{43}
  4. D. -\frac{43}{27} ✓

Correct Answer: D. -\frac{43}{27}

Explanation

Express a and d in terms of a common variable. From the given equations, c = \frac{7}{6}d, b = \frac{5}{4}c = \frac{35}{24}d, and a = 3b = \frac{35}{8}d. Thus, \frac{d+a}{d-a} = \frac{d + \frac{35}{8}d}{d - \frac{35}{8}d} = \frac{\frac{43}{8}d}{-\frac{27}{8}d} = -\frac{43}{27}.

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