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what are all of the positive integer solutions of 7x - 5y = 3 such that x + y belongs to [20, 30] (inclusive) ?

 Nov 11, 2018
 #1
avatar+107405 
+3

I find one

 

[ x, y]  =  [ 9, 12 ]

 

 

 

cool  cool cool

 Nov 11, 2018
 #2
avatar+107520 
+3

Hi Chris 

Once you have one you can find all

7(9)-5(12)=3

7(9+5k)-5(12+7k)=3

See I have added 35k and then taken it away again.

 Nov 12, 2018
 #3
avatar+107520 
+2

Obviously the question only wants the pairs that add to between 20 an 30

So

20<=21+12k<=30

-1<=12k<=9

-1/12 <=k <= 9/12

-1

K= 0

 

There is only the one answer.

Melody  Nov 12, 2018
 #4
avatar+107405 
+1

OK..thanks, Melody.....I see that  !!!

 

 

cool cool cool

CPhill  Nov 12, 2018

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