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Question 1188035: Cindy, Derrick and Edmund had $410 altogether. Cindy gave 1/3 of her money to
Edmund, Derrick then gave 2/5 of his money to Cindy. As a result, Derrick had $20
less than Cindy and $30 less than Edmund. How much money did Cindy have at
first?
Found 3 solutions by josgarithmetic, ikleyn, Solver92311:
Answer by josgarithmetic(39620)   (Show Source):
Answer by ikleyn(52803)  (Show Source):
You can put this solution on YOUR website! .
Cindy, Derrick and Edmund had $410 altogether. Cindy gave 1/3 of her money to
Edmund, Derrick then gave 2/5 of his money to Cindy. As a result, Derrick had $20
less than Cindy and $30 less than Edmund. How much money did Cindy have at first?
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Let solve the problem in a backward manner.
Let x be what Derrick had finally.
Then Cindy had (x+20) dollars at the end; Edmund had (x+30) dollars at the end.
The total is $410; it did not change after these interior changes. So
x + (x+20) + (x+30) = 410
3x + 50 = 410
3x = 410 - 50 = 360
x = 360/3 = 120 dollars.
Thus at final, Derrick had 120 dollars; Cindy had 120+20 = 140 dollars and Edmund had 120+30 = 150 dollars.
Now we will make one step back, from the end to the beginning.
As the problem says, Derrick gave 2/5 of his money to Cindy.
Hence, Derrick left with only 3/5 of his money, and this 3/5 of his original money is 120 dollars.
It means that originally Derrick had  = 5*40 = 200 dollars.
HENCE, Derrick gave 2/5 of $200, or 80 dollars to Cindy.
The problem says: "Cindy gave 1/3 of her money to Edmund".
So, Cindy left with 2/3 of her original money, PLUS 80 dollars she got from Derrick.
So, we write this equation for the Cindy original amount "C"
 = 140 dollars.
We solve this equation easily and get  = 140-80 = 60; hence C =  = 90.
ANSWER. Cindy had 90 dollars, at first.
Solved.
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Solving backward allows to untangle the problem and obtain the solution in a simple manner.
Answer by Solver92311(821)  (Show Source):
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