If (a + b) : (b + c) : (c + a) = 5 : 7 : 6, then what is the value of (a - b + c) : (a + b - c)?
A.1 : 1
B.2 : 3
C.3 : 1✓ Correct
D.4 : 3
Explanation
Let a+b = 5k, b+c = 7k, c+a = 6k. Sum: 2(a+b+c) = 18k, so a+b+c = 9k. Then c = 9k - 5k = 4k, a = 9k - 7k = 2k, b = 9k - 6k = 3k. Now a - b + c = 2k - 3k + 4k = 3k. And a + b - c = 2k + 3k - 4k = k. Ratio = 3 : 1.
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