math

posted by .

Tashana has 16 coins that total to $1.85. She has only nickels, dimes and quarters. How many of each coin could
she have?

  • math -

    nickels --- x
    dimes --- y
    quarters --- 16-x-y

    5x + 10y + 25(16-x-y) = 185
    5x + 10y + 400 - 25x - 25y = 185
    -20x - 15y = -215
    divide by -5
    4x + 3y = 43

    but x and y must be positive integers
    we know the x-intercept is < 11
    and the y-intercept < 14

    y = (43 - 4x)/3
    by inspection, if x = 4 , y = 9 is the only combination that will work
    so she has 4 nickels, 9 dimes and 16-4-9 or 3 quarters.

    check:
    does she have 16 coins ?
    4+9+3 = 16 , yes

    does she have $1.85 ?
    4(5) + 9(10) + 25(3) = 185 , yes!!

  • math -

    She could actualy do it several different combinations.
    5 quarters, 1 dime, and 10 nickels
    4 quarters, 5 dimes, and 7 nickels
    3 quarters, 9 dimes, and 4 nickels
    2 quarters, 13 dimes, and 1 nickel

  • Jeff is right- math -

    Should not have stopped after I found one.

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