If (x + y) : (y + z) : (z + x) = 2 : 3 : 4 and (x + y + z) = 27, then what is…

Correct answer: 15

Let the common multiplier be k. Then:

• x + y = 2k

• y + z = 3k

• z + x = 4k

Add all three equations:

(x + y) + (y + z) + (z + x) = 2k + 3k + 4k

So, 2(x + y + z) = 9k. Since x + y + z = 27, we get 2 × 27 = 9k, so k = 6.

Now x + y = 2k = 12. Therefore:

z = (x + y + z) - (x + y) = 27 - 12 = 15

Final answer: 15