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

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


M×R×O+M^2=46M but M×R×O=240 so

M^2−46M2+240=0 will give us M=6 and M=40 as a whole numbers

In the same way

R^2+R×M×O=64R so

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

To obtain the O values, substituting into M×R×O=240 we obtain
M=6,R=4,O=10
M=6,R=60,O=
M=40,R=4,O=
M=40,R=50,O=

Anser: R+M+O = 20

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