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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: P & C [rates assured]
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[Post New]25 Oct 2007 11:53:46 IST
    Subject: P & C [rates assured]
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pal_sodhi91 (21)

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Q. Find the number of positive integral solutions for :

                     3x+y+z<=30
    
[Post New]25 Oct 2007 12:12:37 IST
    Subject: Re:P & C [rates assured]
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raja987654321 (9)

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For  3x+y+z<=30
          y+z<=30-3x
Now no of positive inteagral solution for this is
      C(29-3x,1)=29-3x (for all x>0 & x I)
  Hence x=1,.....,9
  Thus 9 possible inteagral solutions
                    
   
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[Post New]25 Oct 2007 12:24:01 IST
    Subject: P & C [rates assured]
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fused_bulb (233)

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given condition :: x,y,z>0 & 3x + y + z <=30

=> y+z <= 30-3x
=>ordered pairs of form ( y,z ) which satisfies this is
30 - 3x -1= 29 - 3x

x can vary from 0 t0 9

total solutions = Summation [ 29 - 3x ] ( from x=1 to x=9)

= ( 29x9) - 3x45
=126
............tseb eht ma i
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[Post New]25 Oct 2007 12:24:27 IST
    Subject: P & C [rates assured]
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fused_bulb (233)

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and yeah....do giv me rates... :D
............tseb eht ma i
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[Post New]25 Oct 2007 15:19:47 IST
    Subject: Re:P & C [rates assured]
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raja987654321 (9)

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sry my soln incomplete u need add up the combination results for for the values of x=1,.....,9
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