x,y,z are positive integers. If x(y+z)=63, y(z+x)=40, z(y+x)=33, what is the value of x+y+z?


TCS SkillRack on 16-Mar-2016 11:35

x,y,z are positive integers. If x(y+z)=63, y(z+x)=40, z(y+x)=33, what is the value of x+y+z?
on 17-Mar-2016 17:17

14
on 21-Mar-2016 11:57

12
on 28-Mar-2016 15:21

As we look at the third equations, z = 11 or 3 but, z=11 does not satisfies the other two equations therefore, z=3 => y = 11-x Now, as we see in the second equation, i.e., y(z+x)=40 => (11-x)(3+x)=40 => x=1; y=10 Therefore, x+y+z = 14
Solution:


As we look at the third equations, z = 11 or 3 but, z=11 does not satisfies the other two equations therefore, z=3 => y = 11-x Now, as we see in the second equation, i.e., y(z+x)=40 => (11-x)(3+x)=40 => x=1; y=10 Therefore, x+y+z = 14