Peter and John had some money. If Peter gave John $360, both would have an equal amount of money. If John gave Peter $180, John would have 1/3 as much money as Peter. How much money did Peter have at first?
+26400 Peter and John had some money. If Peter gave John $360, both would have an equal amount of money. If John gave Peter $180, John would have 1/3 as much money as Peter. How much money did Peter have at first?
\(\begin{array}{lrcl} (1) & P-360 &=& J +360 \\ & J &=& P - 720 \\ \hline \\ (2) & \dfrac13 (P+180) &=& J-180 \qquad | \qquad J = P - 720 \\ & \dfrac13 (P+180) &=& P - 720 -180\\ & \dfrac13 (P+180) &=& P - 900\\ & \dfrac{P}{3} +60 &=& P - 900\\ & P-\dfrac{P}{3} &=& 960\\ & \dfrac{2}{3}P &=& 960\\ &P &=& \dfrac32 \cdot 960\\ &P &=& 1440 \end{array}\)
+26400 Peter and John had some money. If Peter gave John $360, both would have an equal amount of money. If John gave Peter $180, John would have 1/3 as much money as Peter. How much money did Peter have at first?
\(\begin{array}{lrcl} (1) & P-360 &=& J +360 \\ & J &=& P - 720 \\ \hline \\ (2) & \dfrac13 (P+180) &=& J-180 \qquad | \qquad J = P - 720 \\ & \dfrac13 (P+180) &=& P - 720 -180\\ & \dfrac13 (P+180) &=& P - 900\\ & \dfrac{P}{3} +60 &=& P - 900\\ & P-\dfrac{P}{3} &=& 960\\ & \dfrac{2}{3}P &=& 960\\ &P &=& \dfrac32 \cdot 960\\ &P &=& 1440 \end{array}\)
