If a : b = c : d = e : f = 4 : 7, then (ma + nc + oe) : (mb + nd + of) is…
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If a : b = c : d = e : f = 4 : 7, then (ma + nc + oe) : (mb + nd + of) is equal to
- A.
1 : 1
- B.
3 : 7
- C.
4 : 7
- D.
5 : 7
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Correct answer: C
Solution: Use the fact that each pair has the same ratio 4:7.
Write a = 4x, b = 7x; c = 4y, d = 7y; e = 4z, f = 7z for some numbers x, y, z.
Compute the numerator: ma + nc + oe = m(4x) + n(4y) + o(4z) = 4(mx + ny + oz).
Compute the denominator: mb + nd + of = m(7x) + n(7y) + o(7z) = 7(mx + ny + oz).
Therefore, (ma + nc + oe) : (mb + nd + of) = 4(mx+ny+oz) : 7(mx+ny+oz) = 4 : 7.