money problem - 2

Let $P$ be the initial amount of Phil's money.

Let $A$ be the initial amount of Anne's money.

$P=3A$ $\implies$ $A=\dfrac{P}{3}$ $\color{#D61F06}(1)$

$P-285=2(A+285)$ $\color{#D61F06}(2)$

Substituting $\color{#D61F06}(1)$ in $\color{#D61F06}(2)$ , we have

$P-285=2\left(\dfrac{P}{3}+285\right)$

$P-285 = \dfrac{2}{3}P + 570$

$\dfrac{P}{3}=855$

$\boxed{P=\$~2565}$

Let $P$ and $A$ be the amount of money Phil and Anne had at first respectively in dollars.

"Phil had 3 times as much money as Anne." $\rightarrow P = 3A \quad \rule[1mm]{1cm}{.1pt} \quad (1)$

"After Phil gave $285 to Anne, he had twice as much money as she did." $\rightarrow P - 285 = 2(A + 285) \quad \rule[1mm]{1cm}{.1pt} \quad (2)$

Substituting $(1)$ into $(2)$ and solving, we get: $\begin{aligned} 3A - 285 &= 2(A + 285) \\ 3A - 285 &= 2A + 570 \\ 3A - 2A &= 570 + 285 \\ A &= 855 \\ P &= 3(855) \\ &= \boxed{2565} \end{aligned}$ Therefore, the answer is 2565 .