SOLUTION: Collin has some change in his pocket. He wants his friend to figure what how many coins he has. Here are the clues. 1) coins equal up to one dollar 2) he has no more than 100 coi

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Question 1032751: Collin has some change in his pocket. He wants his friend to figure what how many coins he has. Here are the clues.
1) coins equal up to one dollar
2) he has no more than 100 coins
3) he has 3 times as many quarters as dimes
4) he had the same number of nickels as quarters.
What coins did he have>

Thank you!

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
We never see any half dollars anymore, so I will exclude them.
1) coins equal up to one dollar
25q+10d+5n+p=100

2) he has no more than 100 coins
q+d+n+p <= 100

3) he has 3 times as many quarters as dimes
q = 3d

4) he had the same number of nickels as quarters.
n = q

25q+10d+5n+p=100

Since q=3d and n=q, substitute 3d for q and n

25(3d)+10d+5(3d)+p=100

75d+10d+15d+p=100

100d+p=100

d could only be 0 or 1

If d=0 then he has 100 pennies.
Yes that's possible, because:

1) coins equal up to one dollar,
 
since 100 pennies is one dollar

2) he has no more than 100 coins
100 pennies is no more than 100 coins

3) he has 3 times as many quarters as dimes
0 times 3 is 0

4) he had the same number of nickels as quarters.
0 = 0

So that's one solution: 100 pennies, 
but it's a funny one!

If d = 1

100d+p = 100

100(1)+p = 100

100+p = 100

    p = 0

The other solution is 1 dime, no pennies and since:

3) he has 3 times as many quarters as dimes
He has 3 quarters, and since

4) he had the same number of nickels as quarters.
He has 3 quarters.

So he has 3 quarters, 1 dime, and 3 nickels,
or the funny answer, 100 pennies.

Edwin