If (x + y) : (y + z) : (z + x) = 2 : 3 : 4 and (x + y + z) = 27, then what is…
2021
If (x + y) : (y + z) : (z + x) = 2 : 3 : 4 and (x + y + z) = 27, then what is the value of z?
Answer: C. 15 — 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…
- A.
10
- B.
17
- C.
15
- D.
12
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Show answer & explanation
Correct answer: C
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
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