SOLUTION: Hi Mark had 80% more money than Bob. Vicky had 40% less than Bob. Mark and Bob gave vicky some money in the ratio of 3;2 respectively. In the end vicky had twice as much money as

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Question 1187717: Hi
Mark had 80% more money than Bob. Vicky had 40% less than Bob. Mark and Bob gave vicky some money in the ratio of 3;2 respectively. In the end vicky had twice as much money as before. Given that Mark had $144 more than vicky in the end how much money did each of them have at first.
Thanks
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Mark had 80% more money than Bob.
m = 1.8b
Vicky had 40% less than Bob.
v = .6b
Mark and Bob gave vicky some money in the ratio of 3;2 respectively.
let a = amt of money m and b gave to v
then their remaining amts:
m = m - .6a
b = b - .4a
In the end vicky had twice as much money as before.
2v = v + a
v - v = a
v = a
Given that Mark had $144 more than vicky in the end
v = a
m - .6v = 2v + 144
m - .6v - 2v = 144
m - 2.6v = 144
how much money did each of them have at first.
find b, replace m with 1.8b, replace v with .6b
1.8b - 2.6(.6b) = 144
1.8b - 1.56b = 144
.24b = 144
b = 144/.24
b = $600 amt the Bob had
then
m = 1.8 * 600
m = $1080 is Mark's amt originally
and
v = .6 * 600
v = $360 is Vicky's amt