SOLUTION: 2 people had 270$ altogether. one person decides to give a quarter of what he has in exchange for a third of what the other person has. as a result of the exchange they both have a

Question 966312: 2 people had 270$ altogether. one person decides to give a quarter of what he has in exchange for a third of what the other person has. as a result of the exchange they both have an equal amount of money. How much did they each have at first?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
2 people had 270$ altogether. one person decides to give a quarter of what he has in exchange for a third of what the other person has. as a result of the exchange they both have an equal amount of money.
How much did they each have at first?
:
let a = amt one person has originally
let b = amt the other person has
therefore
a + b = 270
a = (270-b)
:
"one person decides to give a quarter of what he has in exchange for a third of what the other person has. as a result of the exchange they both have an equal amount of money."
a - .25a + .33b = b - .33b + .25a
.75a + .33b = .67b + .25a
.75a - .25a = .67b - .33b
.50a = .33b
replace a with (270-b)
.50(270-b) = .33b
135 - .5b = .33b
135 = .33b + .5b
135 = .83b
b = 135/.83
b = $162.65 b's amt
then
270 - 162.65 = $107.35 a's amt
:
:
See if they have the same amt
.75(107.35) + .33(162.65) = 134.76
and
.667(162.65) + (.25(107.35) = 135.33; is that close enough?

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