If a : 2b = 5 : 6 and 3a : 2c = 5 : 6, then a : b : c is equal to:
2019
If a : 2b = 5 : 6 and 3a : 2c = 5 : 6, then a : b : c is equal to:
- A.
15 : 25 : 27
- B.
3 : 5 : 9
- C.
5 : 3 : 9
- D.
25 : 15 : 27
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Correct answer: C
Given: a : 2b = 5 : 6 and 3a : 2c = 5 : 6. Find a : b : c.
From a : 2b = 5 : 6, set a = 5k and 2b = 6k, so b = 3k.
From 3a : 2c = 5 : 6, set 3a = 5m and 2c = 6m, so a = 5m/3 and c = 3m.
Equate the two expressions for a: 5k = 5m/3 ⇒ k = m/3.
Express a, b, c in terms of m: a = 5k = 5(m/3) = (5m)/3, b = 3k = 3(m/3) = m, c = 3m.
Clear the fraction by multiplying all terms by 3: a : b : c = 5m : 3m : 9m = 5 : 3 : 9.
Therefore, a : b : c = 5 : 3 : 9.