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3 November, 03:44

Marcus has a change jar that contains only nickels and pennis. He has 65 coins which add up tona total of 1.73. How many of each type of coins does he have.

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  1. 3 November, 04:03
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    Question: How many nickels and pennies when there are 65 coins that add up to a value of 1.73?

    A. solution requiring no pencils, no calculators

    If all coins are pennies, it would be worth 0.65, with (1.73-0.65) = 1.08 left over.

    We can change a nickel for a penny for (0.05-0.01) = 0.04 (4 cents), so

    number of nickels = 1.08/0.04=27

    number of pennies = 65-27=38

    Answer there are 38 pennies and 27 nickels

    B. solution using a linear equation

    Let n=number of nickels, then (65-n) = number of pennies.

    Total value (cents) = 173 = 5n + (65-n) = 65+4n

    Solve for n = (173-65) / 4=27 (number of nickels)

    and (65-n) = 38 (number of pennies.

    Answer there are 38 pennies and 27 nickels

    C. solution using a system of equations

    Let

    n=number of nickels

    p=number pennies

    Total number of coins

    n+p=65 ... (1)

    Total value in cents

    5n+p=173 ... (2)

    Solve for n and p

    (2) - (1)

    5n-n+p-p=173-65

    4n=108

    n=27 (27 nickels)

    p+n=65

    p=65-n=65-27=38 (38 pennies)

    Answer there are 38 pennies and 27 nickels
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