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algebra

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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?

  • algebra - ,

    4 pennies
    1 nickle
    2 dimes
    3 quarters

  • algebra - ,

    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
    45-49 -------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
    70-74 --- 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
    85-89 --- 3 quarters, 1 dime, 4 pennies
    90-94 --- 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

  • go with bobpursley - algebra - ,

    ARRGGGHHHH!!!!

    looks like I messed up in my 45-49
    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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