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Find the number of positive integer solutions to 2x + 3y = 100.

 May 4, 2020
 #1
avatar+651 
+1

N = 16.

So, 16 positive integer solutions are possible for this equation.

 

coolsmileycool

 May 4, 2020
 #2
avatar+111430 
+1

2x + 3y  = 100

 

3y  =  100 - 2x

 

y  =  100 - 2x

       _______

             3

 

We can only have integer solutions for y  whenever  x  = 2 , 5, 8, 11, etc

 

And the last  x  that  makes y a positive integer  is  when x  = 47

 

So....the  number  of  integers  =   [ 47 - 2 ] / 3  + 1   =   45 / 3 + 1   =   15  + 1  =  16

 

Just as Lucky Ducky found   !!!!!

 

GOOD JOB LUCKYDUCKY  !!!!!

 

cool cool cool

 May 4, 2020
 #3
avatar+651 
+1

Thanks!

LuckyDucky  May 4, 2020

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