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a box containing pens,nickels,and dimes has 13 coins with a total value of 83 cents.how many coins of each type are in the box?

  • maths -

    number of pennies --- p
    number of nickels ---- n
    number of dimes ---- 13-p-n

    p + 5n + 10(13-p-n) = 83
    p + 5n + 130 - 10p - 10n = 83
    -9p - 5n= -47
    9p + 5n = 47 ---> n = (47-9p)/5
    since both p and n have to be positive integers
    0 < p < 5 and 0 < n< 10

    try p=1 , n is a fraction
    p = 2, n is a fraction
    p=3 , n = 4
    p = 4 , n is a fraction

    so p = 3, n = 4 and subbing back, dimes = 6

    check" 3(1) + 4(5) + 6(10) = 83

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