algebra
posted by linda .
How many coins
When i dumped the change out of my pocket, I noticed that i could pay the exact price for any item from one cent up to and through one dollar without receiving any change. What is the fewest number of coins I could have had in my pocket if i had pennies, nickels, dimes, and quarters? What are the coins?

4 pennies
1 nickle
2 dimes
3 quarters 
start with
4 pennies, 2 nickels , 2 dimes , 3 quarters
covers from
1 to 9  1 nickel, 4 pennies
10 to 14  1 dime, 4 pennies
15 to 19 = 1 dime, 1 nickel, 4 pennies
20 to 24 = 1 dime, 2 nickels 4 pennies OR 2 dimes 4 pennies
25 to 29  1 quarter, 4 pennies
30 to 34  1 quarter, 1 nickel, 4 pennies
35 to 39  1 quarter, 1 dime, 4 pennies
40 to 44  1 quarter, 1 nickel, 1 dime, 4 pennies
4549 1 quarter, 2 nickels 1 dime, 4 pennies
50  54  1 quarter, 2 dimes, 1 nickel, 4 pennies
55  59  2 quarters, 1 nickel, 4 pennies
60  64  2 quarters, 1 dime, 3 pennies
65  69  2 quarters , 1 dime, 1 nickel, 4 pennies
7074  2 quarters, 2 dimes, 4 pennies
75 79  2 quarters, 2 dimes, 1 nickel, 4 pennies
80  84  2 quarters, 2 dimes, 1 nickel, 4 pennies OR 3 quarters, 1 nickel, 4 pennies
8589  3 quarters, 1 dime, 4 pennies
9094  3 quarters, 1 dime, 1 nickel, 4 pennies
95 99  3 quarters , 2 dimes, 4 pennies
100  3 quarters, 2 dimes, 1 nickel
to do 95  99 with only 2 quarters would need
2 quarters, 4 dimes, 1 nickel, 4 pennies
so I could cover any amount from 1 to 100 with
a) 4 pennies, 2 nickels, 2 dimes, and 3 quarters. for a total of 11 coins
or
b) 4 pennies, 2 nickels, 4 dimes, and 2 quarters for a total of 12 coins
Therefore:
4 pennies
2 nickels
2 dimes
3 quarters or a total of 11 coins 
ARRGGGHHHH!!!!
looks like I messed up in my 4549
could be done with 1 quarter, 2 dimes, and 4 pennies.
Nowhere else do we actually need 2 nickels
so as bobpursley said
3 quarters,
2 dimes
1 nickel
4 pennies for a total of 10 coins
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