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Linear equation strange problem

  1. Dec 3, 2014 #1

    Rectifier

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    Gold Member

    The problem
    Adam is saving 1, 5 and 10 dollar bills. Adam has 165 bills. The amount of one dollar bills is twice as high as 10-dollar bills. The total value of his savings is 735 dollars. How many 5-dollar bills does Adam have?

    This problem was translated. Sorry for grammatical errors.

    The attempt at a solution
    x = one dollar bills
    y = five dollar bills
    z = ten dollar bills

    The amount of bills is:
    ## x+y+z=165 ##
    We also know that:
    ##2x = z## which means that the amount of bills can be rewritten as:
    ## x+y+2x=165 \\ y+3x=165##

    The value of his savings is:
    ## 1 \cdot x + 5 \cdot y + 10 \cdot z = 735 ##

    I insert ##2x = z## in the second equation and get following:
    ## 1 \cdot x + 5 \cdot y + 10 \cdot 2x = 735 \\ x + 5y + 20x = 735 \\ 5y + 21x = 735 \\ ##

    I solve the linear equation of
    ## y+3x=165 \\ 5y + 21x = 735 ##

    ## 7y+21x=1155 \\ 5y + 21x = 735 ##

    ## 21x=1155-7y \\ 21x = 735-5y ##

    ## 735-5y=1155-7y \\ 2y=1155-735 \\ 2y= 420 \\ y = 210 ##
    Which is clearly wrong. y (is 5 dollar bills) 5 * 210 = 1050 (but Adams value is 735)

    I have tried some other methods but I cant seem to solve this problem. Please help :,(
     
  2. jcsd
  3. Dec 3, 2014 #2

    Mark44

    Staff: Mentor

    To be clearer, each of the above should say "the number of ..."
    No, this is wrong. What is stated is that the number of one-dollar bills is twice as large as the number of ten-dollar bills. This translates into an equation as x = 2z. You have 2x = z, which is wrong.
     
  4. Dec 3, 2014 #3

    Rectifier

    User Avatar
    Gold Member

    Oh!!! Thank you for finding the error! ;D
     
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