Natalie has some nickels, Dirk has some dimes, and Quincy hassome quarters. Dirk

Question

Natalie has some nickels, Dirk has some dimes, and Quincy hassome quarters. Dirk has five more dimes than Quincy has quarters.If Natalie gives Dirk a nickel, Dirk gives Quincy a dime, andQuincy gives Natalie a quarter, they will all have the same amountof money. How many coins did each have originally? Please use an equation to solve. Thank you! :) Natalie has some nickels, Dirk has some dimes, and Quincy hassome quarters. Dirk has five more dimes than Quincy has quarters.If Natalie gives Dirk a nickel, Dirk gives Quincy a dime, andQuincy gives Natalie a quarter, they will all have the same amountof money. How many coins did each have originally? Please use an equation to solve. Thank you! :)

Explanation / Answer

We don't know anything about Natalie so just forget about her fornow, we know things about dirk and quincy and we know that Nataliehas to end up with the same amount of money as them. let x = number of coins Dirk has         (x+5)(.10)    amount of money Quincy has .25x             amount of money after the exchanges (x+5) (.10) + .05 - .10 = .25x + .10 - .25 .10x + .45 = .25x - .15 .60 = .15x x = 4 coins, this means that : Quincy had 4 quarters = $1.00 to start out (x+5) = 9 coins this means that: Dirk had 9dimes         = $ .90 tostart out After exchanging: Quincy had .25(4) + .10 - .25 = $.85 Dirk had (x+5)(.10)+.05-.10 = $.85 and according to the problem Natalie also had to have $.85 afterthe exchange before the exchange, Natalie had $.85 - $.25 + .05 = $.55    ( she gained a quarter and lost anickel) This means that since Natalie only started with nickels, she had.55/.05 = 11 nickels to start Then Originally: Quincy had 4 quarters Dirk had 9 dimes Natalie had 11 nickels I hope this helps, Please RATE and COMMENT!!

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