SOLUTION: Coin question 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 g

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Question 896368: Coin question
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 have originally?
I set up an equation to show how much money Dirk has: .10d + .05 - .10 where d is the number of dimes. For Quincy: .25q + .10 - .25 where q is the number of quarters. I also set up 5 + d = q to show that Dirk has 5 more coins than Quincy then I solved for d (d = q - 5) and substituted that in Dirks formula, but this isn't working. I know intuitively that they each end up with $.85 and that means Natalie has 13 coins, Dirk has 9 and Quincy has 4 at the beginning, but I can't figure out how to write this as an equation. I appreciate the help, Judy
Found 3 solutions by rothauserc, ankor@dixie-net.com, Edwin McCravy:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website!
Dirk has (x+5).10
Quincy has x(.25)
Natalie has (y-1).05
Dirk has .05 + (x+5).10
Dirk has .05 + (x+4).10
Quincy has x(.25) +.10
Quincy has (x-1).25 +.10
Natalie has (y-1).05 +.25
now we can write the final equations
Dirk = Natalie = Quincy
.05 + (x+4).10 = (y-1).05 +.25 = (x-1).25 +.10
.05 +.10x +.40 = .05y -.05 +.25 = .25x -.25 +.10
.10x +.45 = .05y +.20 = .25x -.15
first solve for x
.10x +.45 = .25x - .15
-.15x = -.60
x = 4
now we can solve for y
.05 + (4+4).10 = (y-1).05 +.25
.85 = .05y -.05 + .25
.85 = .05y +.20
.05y = .65
y = 13
Dirk had 9 dimes, Quincy had 4 quarters and Natalie had 13 nickels

Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!
Natalie has some nickels, Dirk has some dimes and Quincy has some quarters.
Dirk has five more dimes than Quincy has quarters.
d = q + 5
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.
.10d + .05 - .10 = .25q +.10 - .25
.10d -.05 = .25q - .15
.10d = .25q -.15 + .05
.10d = .25q - .10
multiply by 10
d = 2.5q - 1
we know that d = q + 5
q + 5 = 2.5q - 1
5 + 1 = 2.5q - q
6 = 1.5q
q = 6/1.5
q = 4 quarters
then
d = 4 + 5 = 9 dimes
:
Find n:
.05n -.05 + .25 = .05n + .20
we know that
.05n + .20 = .25q -.15
Replace q with 4
.05n + .20 = 1.0 - .15
.05n = .85 - .20
.05n = .65
n = .65/.05
n = 13 nickels

How many coins did each have originally?

Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
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.

Let's avoid decimals by using cents rather than dollars. Natalie has N nickels. She has 5N cents Dirk has D dimes. He has 10D cents Quincy has Q quarters. So he has 25Q cents.

Dirk has five more dimes than Quincy has quarters.

So D = Q+5 So in the beginning, Natalie has 5N, Dirk has 10D, and Quincy has 25Q.

...Natalie gives Dirk a nickel,

Natalie now has 5N-5, Dirk now has 10D+5, and Quincy still has 25Q.

Dirk gives Quincy a dime,

Natalie still has 5N-5, Dirk now has 10D+5-10, and Quincy now has 25Q+10

and Quincy gives Natalie a quarter;

Natalie now has 5N-5+25, Dirk still has 10D+5-10 and Quincy now has 25Q+10-25

they will all have the same amount of money.

Therefore 5N-5+25 = 10D+5-10 = 25Q+10-25 5N+20 = 10D-5 = 25Q-15 Since D = Q+5 5N+20 = 10(Q+5)-5 = 25Q-15 10Q+50-5 = 25Q-15 10Q+45 = 25Q-15 60 = 15Q 4 = Q Since D = Q+5 D = 4+5 D = 9 5N+20 = 10D-5 5N+20 = 10(9)-5 5N+20 = 90-5 5N+20 = 85 5N = 65 N = 13 Checking (using dollars) Natalie has 13 nickels or $0.65 Dirk has 9 dimes or #0.90 Quincy has 4 quarters or $1.00

Dirk has five more dimes than Quincy has quarters.

That checks since 9 = 4+5 So in the beginning, Natalie has $0.65, Dirk has $0.90, and Quincy has $1.00.

...Natalie gives Dirk a nickel,

Natalie now has $0.60, Dirk now has $0.95, and Quincy still has $1.00.

Dirk gives Quincy a dime,

Natalie still has $0.60, Dirk now has $0.85, and Quincy now has $1.10

and Quincy gives Natalie a quarter;

Natalie now has $0.85, Dirk still has $0.85 and Quincy now has $0.85

They all have the same amount of money, 85 cents. So the answer is correct.

Edwin