Going To The Picnic

Going To The Picnic

Let p = people
Let w = wagon

$\begin{array}{|lrcll|} \hline (1) & p &=& (w-10)(\frac{p}{w}+1) \\ & p &=& p + w - 10\frac{p}{w}-10 \\ & 0 &=& w - 10\frac{p}{w}-10 \\ & 10\frac{p}{w} &=& w -10 \\ &\mathbf{ p } & \mathbf{=} & \mathbf{\frac{w}{10} (w -10) } \\\\ (2) & p &=& (w-25)(\frac{p}{w}+3) \\ & p &=& p+3w - 25\frac{p}{w}-75 \\ & 0 &=& 3w - 25\frac{p}{w}-75 \\ & 25\frac{p}{w} &=& 3w-75 \\ &\mathbf{ p } & \mathbf{=} & \mathbf{\frac{w}{25} (3w-75) } \\ \hline \end{array}$

$\begin{array}{|rcll|} \hline p= \mathbf{\frac{w}{10} (w -10) } &\mathbf{=}& \mathbf{\frac{w}{25} (3w-75) } \\ \frac{w}{10} (w -10) &=& \frac{w}{25} (3w-75) \\ 25 (w -10) &=& 10 (3w-75) \\ 5 (w -10) &=& 2 (3w-75) \\ 5w-50 &=& 6w-150 \\ \mathbf{ w } &\mathbf{ =}& \mathbf{ 100 } \\ \hline \end{array}$

$\begin{array}{|rcll|} \hline \mathbf{ p } & \mathbf{=} & \mathbf{\frac{w}{10} (w -10) } \\ &=& \frac{100}{10} (100 -10) \\ &=& 10\times 90 \\ \mathbf{ p } &\mathbf{ =}& \mathbf{ 900 } \\ \hline \end{array}$

Correct, heureka...!!!!