SOLUTION: 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

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 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      Log On


   

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?
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39628) About Me  (Show Source):
You can put this solution on YOUR website!
KEVIN       k       (k-54)/j=2/5

JAMES       j        k/(j-54)=8/13

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
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.