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

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Answer 1 · 2016-11-27T16:11:54

$20$ $20$

Multiplying $R \times O + M = 46$ $R xx O + M = 46$ term to term by $M$ $M$ we have

$M \times R \times O + M^{2} = 46 M$ $M xx R xx O + M^2= 46 M$ but $M \times R \times O = 240$ $M xx R xx O = 240$ so

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

In the same way

$R^{2} + R \times M \times O = 64 R$ $R^2+R xx M xx O=64 R$ so

$R^{2} - 64 R + 240 = 0$ $R^2-64R+240=0$ will give us $R = 4$ $R=4$ and $R = 60$ $R=60$

To obtain the $O$ $O$ values, substituting into $M \times R \times O = 240$ $M xx R xx O = 240$ we obtain

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

so the solution is

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

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