If x, y, and z are positive integers and 3x=4y=7z, then the least possible value of x+y+z is
I used the following approach in order to try and solve this problem:
First I set all variable in terms of x which resulted in
x+y+z = x+(3/4)x+(3/7)x
simplifying, x+(3/4)x+(3/7)x = (61/28)x
This is where I got stuck. Any suggestions?
you are almost there
now x + y + z will be a +ve integer since x,y, and z each are +ve integers.
so (61/28)x will be a integer => x is a multiple of 28.
now (61/28)x will be minimum when x = 28
hence x+y+z = 61