Results 1 to 3 of 3

Math Help - need help for my math problem

  1. #1
    Junior Member
    Joined
    Jun 2014
    From
    Brighton
    Posts
    38
    Thanks
    2

    need help for my math problem

    A person went to a bank to cash a check. In handing over the money the cashier, by mistake, gave him dollars for cents and cents for dollars. He kept the money in his pocket without examining it, and spent a nickel on his way home. He then found that he has exactly twice the amount of the check. He had no money in his pocket before going to the bank. What was the exact amount of that check?

    Please give me the solution for this puzzle and tell me how to solve it also?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,130
    Thanks
    337

    Re: need help for my math problem

    Let C = number of cents on the check and D = number of dollars. The amount of money he should have received in cents is 100D + C, but he actually receved 100C + D. So after spending the nickel and realizing he has twice as much money as he should have the equation you need to solve is:

    100C + D - 5 = 2(100D +C)

    Rearrange: 98C = 199D + 5

    Both C and D must be integers, and both must be in the range (0,99) inclusive. At this point you can use trial and error, but first note that the left side is even, which means 199D must be odd, so D is odd. Also, since 98 has prime factors 2 and 7, D cannot be a multiple of 7 (since 199D +5 would not be a multiple of 7). After that, I think it's just trial and error to find integer solutions for C and D, but to save you a little time I suggest you start with trying D = 25, then 27, etc. - you should get it shortly
    Last edited by ebaines; June 25th 2014 at 09:05 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jun 2014
    From
    Brighton
    Posts
    38
    Thanks
    2

    Re: need help for my math problem

    Quote Originally Posted by ebaines View Post
    Let C = number of cents on the check and D = number of dollars. The amount of money he should have received in cents is 100D + C, but he actually receved 100C + D. So after spending the nickel and realizing he has twice as much money as he should have the equation you need to solve is:

    100C + D - 5 = 2(100D +C)

    Rearrange: 98C = 199D + 5

    Both C and D must be integers, and both must be in the range (0,99) inclusive. At this point you can use trial and error, but first note that the left side is even, which means 199D must be odd, so D is odd. Also, since 98 has prime factors 2 and 7, D cannot be a multiple of 7 (since 199D +5 would not be a multiple of 7). After that, I think it's just trial and error to find integer solutions for C and D, but to save you a little time I suggest you start with trying D = 25, then 27, etc. - you should get it shortly
    Thank you for reply
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Math problem
    Posted in the Algebra Forum
    Replies: 4
    Last Post: November 2nd 2012, 08:36 AM
  2. Math problem
    Posted in the Number Theory Forum
    Replies: 6
    Last Post: March 2nd 2010, 08:36 AM
  3. Math Problem Help!
    Posted in the Algebra Forum
    Replies: 5
    Last Post: June 14th 2009, 09:30 PM
  4. i need help with math problem
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: January 23rd 2007, 09:43 AM
  5. A Math Problem!! Help
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: December 19th 2005, 04:13 PM

Search Tags


/mathhelpforum @mathhelpforum