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If x , y ,and z are positive , with xy =...

If x , y ,and z are positive , with xy = 24 , xz = 48 , and yz = 72 , then x + y + z =

A

22

B

36

C

50

D

62

Text Solution

Verified by Experts

The correct Answer is:
A
First evaluate the ratio `(xy)/(xz) = (y)/(z) = (24)/(48) = (1)/(2)` . Cross - multiply to get z = 2y , and substitute in the third equation : `yz = y (2y) = 2y^2 = 72 `. Therefore , y = 6 , z = 12 , and x = 4 and x + y + z = 22 .
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