Question

The letters `R, M, O` represent whole numbers. If `RxxMxxO=240, RxxO+M=46, R+MxxO=64`, then what is the value of `R+M+O`?

Answer 1

`20`

Explanation:

Multiplying `R xx O + M = 46` term to term by `M` we have

`M xx R xx O + M^2= 46 M` but `M xx R xx O = 240` so

`M^2-46M^2+240=0` will give us `M=6` and `M = 40` as a whole numbers

In the same way

`R^2+R xx M xx O=64 R` so

`R^2-64R+240=0` will give us `R=4` and `R=60`

To obtain the `O` values, substituting into `M xx R xx O = 240` we obtain

`((M,R,O),(6,4,10),(6,60,-),(40,4,-),(40,60,-))`

so the solution is

`M+R+O=6+4+10=20`