<PRE><B>Question 826654</B>
if x,y and z are positive integers with xy=18, xz=3 and yz=6,
 what is the value of x+y+z?
;
Rearrange the equations and substitute
xy = 18
y = {{{18/x}}}
:
xz = 3
z = {{{3/x}}}
:
yz = 6
replace y with 18/x and replace z with 3/x
{{{18/x}}}*{{{3/x}}} = 6
{{{54/x^2}}} = 6
54 = 6x^2; multiplied both sides by x^2
{{{54/6}}} = x^2; divided both sides by 6
9 = x^2
x = {{{sqrt(9)}}} 
x = 3
then
3y = 18
y = 6
and
6z = 6
z = 1
Find x + y + z
3 + 6 + 1 = 10
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