SOLUTION: If x, y, and z are positive integers with xy=24, xz=48, and yz=72, find x+y+z.

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: If x, y, and z are positive integers with xy=24, xz=48, and yz=72, find x+y+z.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 370459: If x, y, and z are positive integers with xy=24, xz=48, and yz=72, find x+y+z.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
If x, y, and z are positive integers with xy=24, xz=48, and yz=72, find x+y+z.
system%28yz=72%2Cxy=24%29

Divide equals by equals:

yz%2Fxy=72%2F24
z%2Fx=3
z=3x
z%2F3=x

system%28xz=48%2Cxy=24%29

Divide equals by equals:

xz%2Fxy=48%2F24
z%2Fy=2
z=2y
z%2F2=y

system%28z%2F3=x%2Cz%2F2=y%29

Multiply equals by equals:

z%5E2%2F6=xy

Substitute 24 for xy

z%5E2%2F6=24
z%5E2=144
z=12

Substitute 12 for z in

xz=48
x%2812%29=48
12x=48
x=4

Substitute 4 for x in

xy=24
4y=24
y=6

x=4  y=6  z=12

Therefore x+y+z = 4+6+12 = 22

Edwin