COINS
In how many ways can 19 coins
equal exactly one dollar?
When I began to think of strategies
for tackling this problem, I first thought about how many of each
coin would be needed to equal exactly one dollar.
The coins used
are the penny, nickel, dime, quarter, and half-dollar.
How many of each coin is
needed to equal one dollar?
| penny
- 1 cent |
100 pennies |
| nickel
- 5 cents |
20
nickels |
| dime - 10
cents |
10 dimes |
| quarter
- 25 cents |
4 quarters |
| half-dollar
- 50 cents |
2 half-dollars |
Since the amount
of nickels needed to equal one dollar is the closest number to
19, I decided to use nickels as my starting point for my
investigation.
I used a spreadsheet
to organize the different combinations that can be made using
19 coins to equal exactly one dollar.
As stated earlier,
20 nickels equals one dollar. The amount of coins, however, exceeds
19. If we look at only 19 nickels, we indeed have 19 coins, but
we do not have the value of one dollar. So I began my spreadsheet
by looking at the value of 18 nickels.
18 nickels and
1 dime equals exactly one dollar. I continued this trial and error
process by consecutively reducing the number of nickels in my
combinations. By using this process, I found nine different
ways that 19 coins can equal exactly one dollar.
Click HERE
to view my spreadsheet in Excel.
Reference: Dr.
Jim Wilson's EMAT 6600 Page
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