Question

If Owen gives $40 to Charley, they will have an equal amount of money. If Charley gives $80 to Owen, the ratio of Owen’s money to Charley’s money will be 4 : 1. How much money does Owen have in the beginning?

Answer 1

Owen initially had $240.

Explanation:

Let `x` be the amount of money Owen has initially. Let `y` be the amount of money Charley has initially.

If Owen gives $40 to Charley, they will have an equal amount of money:
`x-40 = y+40`

If Charley gives $80 to Owen, the ratio of Owen's money to Charley's money will be 4:1:
`(x+80) /(y-80)=4`

This gives us two equations:
(1) `x-y = 80`
(2) `x-4y=-400`

From (1) we get:
(3) `x = y+80`

Substituting (3) in (2):
`y+80 - 4y = -400`
`-3y = -480`
(4) `y = 160`

Substituting (4) in (1):
`x-160=80`
`x=240`

Hence, Owen initially had $240.