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If a : b = c : d = e : f = 5 : 7, then what is the value of (3a + 5c + 11e) : (3b + 5d + 11f)?

1. 11 : 7
2. 3 : 7
3. 7 : 11
4. 5 : 7

Correct answer: 5 : 7

Solution

Since a:b = c:d = e:f = 5:7, let a=5k, b=7k, c=5k, d=7k, e=5k, f=7k. Then (3a+5c+11e) = k(15+25+55) = 95k and (3b+5d+11f) = k(21+35+77) = 133k. Ratio = 95:133 = 5:7.

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