# 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?

Nov 27, 2016

$20$

#### Explanation:

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

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

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

In the same way

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

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

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

$\left(\begin{matrix}M & R & O \\ 6 & 4 & 10 \\ 6 & 60 & - \\ 40 & 4 & - \\ 40 & 60 & -\end{matrix}\right)$

so the solution is

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