# How do you make \$1.00 with 21 coins?

• Mar 29th 2007, 11:49 PM
veltel
How do you make \$1.00 with 21 coins?
Help Me plase

Thank you
• Mar 30th 2007, 02:39 AM
malaygoel
10*8 + 2*7 + 1*6=100
• Mar 30th 2007, 04:03 AM
topsquark
Quote:

Originally Posted by malaygoel
10*8 + 2*7 + 1*6=100

What coins are these?

I don't have anything better than trial and error, but I'd set it up like this:
Let there be q quarters, d dimes, n nickels, and p pennies. Then:
100 (cents) = 25q + 10d + 5n + 1p

and

q + d + n + p = 21

Solve the second equation for p:
p = 21 - q - d - n

and insert this value of p into the first equation:
100 = 25q + 10d + 5n + (21 - q - d - n)

79 = 24q + 9d + 4n

I would start with the assumption there are 3 quarters (which almost certainly won't work), and work my way down. It could take a while without some more insight, which I'm afraid I can't offer you. :(

-Dan
• Mar 30th 2007, 07:48 AM
ThePerfectHacker
I am not sure what coins are you using.

If you have a lot of coints it becomes the Frobenius Coin Problem.
• Mar 30th 2007, 11:55 AM
Soroban
Hello, veltel!

We have: . Q + . D .+ . N + P .= . 21
. . .and: .25Q + 10D + 5N + P .= .100

Subtract: .24Q + 9D + 4N .= .79

From here, I found four solutions:

. . 2Q, 3D, 1N, 15P
. . 1Q, 3D, 7N, 10P
. . . . . 7D, 4N, 10P
. . . . . 3D, 13N, 5P