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algebra

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Money Mixtures. Elaine has $194, consisting of $20, $5, and $1 bills. The number of $1 bills is 1 less than the total number of $20 and $5 bills. If she has 39 bills in her purse, how many of each denomination does she have?

  • algebra -

    I have already solved two problems like this for you. Set up the algebraic equations that describe what you know, and solve them. There will always be as many independent equations as there are unknowns.

  • algebra -

    number of $20's ---- x
    number of $5's ----- y
    number of $1's ----- z

    but z = x+y - 1

    x+y+z = 39
    x + y + x+y-1 = 39
    2x + 2y = 40
    x + y = 20 (#1)

    also

    20x + 5y + z = 194
    20x + 5y + x+y-1 = 194
    21x + 6y = 195
    7x + 2y = 65 (#2)

    double #1 and subtract fron #2
    5x = 25
    x = 5
    then in x+y = 20 , ----> y = 15
    and finally
    z = x+y-1 = 19

    check: is 5+15+19 = 39 ? YES
    is 20(5) + 5(15) + 19 = 195 ? YEA!!

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