`x/50 + 6 = (300-x)/75 + 7`
`(x+300)/50 = (300 -x + 525)/75`
`(3x+900)/150 = (1650 - 2x)/150`
`3x + 900 = 1650 - 2x`
`5x = 750`
`=> x = 750/5 = 150`.
\(\Leftrightarrow\dfrac{x+6\cdot50}{50}=\dfrac{300-x+7\cdot75}{75}\Leftrightarrow\dfrac{(x+300)\cdot75}{50\cdot75}=\dfrac{\left(825-x\right)\cdot50}{75\cdot50}\)
\(\Leftrightarrow\left(x+300\right)\cdot75=\left(825-x\right)\cdot50\Leftrightarrow75x+22500=825\cdot50-50x\)
\(\Leftrightarrow125x=18750\Leftrightarrow x=150\)