Tuesday, September 23, 2008

Problem Of The Week 24

Let x,y be positive integers such that 19x+90+8y=1998. Let a be the max value of x and b  the max of y.

Find a+b.

6 comments:

  1. x = 100 y = 41

    a+b=141

    ReplyDelete
  2. Sorry! The answer is :: 229 for x =100 and y = 229

    i used the funda ::

    ax+by = k

    Get any value of (x,y) which satisfies the equation and then the next solution i.e x1,y1 is (x +- coeff of y ) (y+- coeff of x)

    here x will decrease by 8 and y will increase by 19.

    the last value which wud satisfy is x=4 and y = 229

    Regards!

    ReplyDelete
  3. yupp 329 is righlty done
    100 is easy
    229 is just a bit more :)

    ReplyDelete
  4. Can somebody explain how the correct answer is 329 ?

    ReplyDelete
  5. Riya its pretty simple
    for x max can be easily found to be 100
    as 1900+90+8=1998
    now case 2
    19x+90+8y=1998
    as all terms are even so is x
    we check for x=2 does not give integer y
    we check for x=4 gives y=229

    we are done here

    ReplyDelete