Question 1206156
Kevin and James each has some money. If only Kevin spends $54, the ratio of the amount of money Kevin has to the amount of money James has will become 2:5. If only James spends $54, the ratio will become 8:13. How much money does each boy have?


Let Kevin have $x
Kevin spends $54
He has a balance of (x-54)

and James have $y

the ratio of the amount of money Kevin has to the amount of money James has will become 2:5
(x-54)/y = 2/5

2y = 5(x-54)

2y= 5x-=-270
2y-5x = =-270........................................1

 If only James spends $54, the ratio will become 8:13.
x/(y-54) =8/13

13x = 8(y-54)
13x = 8y -432
13x -8y = -432....................................2

Multiply (1) by 4 and add the equation to (2)
8y-20x = -1080
13x -8y = -432

-7x = -1512

x = 216

2y = 5(x-54)

substitute x =218

2y = 5(216-54)

2y=162*5

y= 81*5= 405

Kevin has $216 and James has $405.