How Many Coins Did Each Originally Have?Date: 10/22/2001 at 21:46:37 From: kayla Subject: I need help! I am totally stuck - I have no idea how to solve this problem: Natalie has some nickels, Dirk has some dimes, and Quincy has some quarters. Dirk has five more dimes than Quincy has quarters. If Natalie gives Dirk a nickel, Dirk gives Quincy a dime, and Quincy gives Natalie a quarter, they will all have the same amount of money. How many coins did each originally have? Please help me Date: 10/23/2001 at 00:41:58 From: Doctor Ian Subject: Re: I need help! Hi Kayla, We know that Quincy has some number of quarters, but we don't know how many, so let's say he has Q quarters. Similarly, let's say that Dirk has D dimes, and Natalie has N nickels. In terms of cents, the amount of money that each person has is Quincy: 25 * Q Dirk: 10 * D Natalie: 5 * N What else do we know? We know that D is 5 more than Q, right? So D = Q + 5 and in fact, this means that we can forget about D altogether: Quincy: 25 * Q Dirk: 10 * (Q + 5) Natalie: 5 * N Now, the exchanges begin. Let's keep track of what happens. First, Natalie gives Dirk a nickel: Quincy: 25 * Q Dirk: 10 * (Q + 5) + 5 Natalie: 5 * N - 5 Next, Dirk gives Quincy a dime: Quincy: 25 * Q + 10 Dirk: 10 * (Q + 5) + 5 - 10 Natalie: 5 * N - 5 Finally, Quincy gives Natalie a quarter: Quincy: 25 * Q + 10 - 25 Dirk: 10 * (Q + 5) + 5 - 10 Natalie: 5 * N - 5 + 25 Now they all have the same amount of money. Well, if Dirk and Quincy have the same amount of money, then Quincy has: Dirk has: 25 * Q + 10 - 25 = 10 * (Q + 5) + 5 - 10 If you solve this for Q, you'll know how many quarters Quincy started out with, which you can use to find out everything else. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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