Ratio and the equality of money

Question

Bernice and Lily have some money. If Bernice gives Lily \$120, they will have an equal amount of money. If Lily gives Bernice \$120, the ratio of the amount of Bernice's money to the amount of Lily's money will become 4:1. How much money does each of them have?

Answer 1

$x$ is the money Bernice has. $y$ the other's.

First sentence : We have $$x-120=y+120$$ Second sentence : $$\frac{x+120}{y-120}=4$$ or $$x+120=4\left(y-120\right)$$

Two equations ,two unknowns. Substract the last equation to the first one : $$240=4\left(y-120\right)-y-120$$ Thus, $$y=280$$ $$x=520$$