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algebra

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Johnny has $147 dollars in ten, five and one dollar bills. He has 38 bills. He has twice as many fives as tens. He has three more ones than fives. How many of each bill does he have?

  • algebra - ,

    number of tens -- x
    number of fives -- y
    number of ones -- 38-x-y

    10x + 5y + 1(38-x-y) = 147
    9x + 4y = 109
    x and y must be integers.
    sketch 9x + 4y = 108
    x-intercept is 12
    y-intercept is 27

    y = (109-9x)/4 , we know 0 < x < 12
    after some trial and error, x = 9 (only had to try odd x's)

    x = 9
    y = 7

    9 tens
    7 fives and
    22 ones

    check: 90 + 35 + 22 = 147

  • algebra - ,

    Let x = $5, then x+3 = $1 and .5x = $10. Then:

    x + (x+3) + .5x = 38

    2.5x = 35

    x = 14, x+3 = 17 and .5x = 7

    To check:

    5*14 + 17 + 10(7) = 147

    157 ≠ 147

    It doesn't check. Do you have typo?

  • oops - algebra - ,

    Should have read the question more carefully, looks like I anticipated the question.

    tens --- x
    fives --- 2x, it said so
    ones -- 2x+3

    10x + 5(2x) + 1(2x+3) = 147
    22x = 144
    x = 144/22 , which is not a whole number

    There is no solution.

    I agree with PsyDAG

  • algebra - ,

    Thanks! No typo, it must just be another trick up my teacher's sleeve!

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