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How many ordered pairs (x,y) of positive integers satisfy the inequality 4x+5y < 120?

 Aug 1, 2022
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When y =  1

x ranges from  1  to  28

 

When y = 2

x ranges from  1 to  27

 

When y = 3

x  ranges from 1 to  26

 

...

 

When y = 22

x ranges from 1 to 2

 

When y = 23

x  only has the value 1

 

So the  number  of  positive integer  values  = the sum of the first  28 positive integers  =

 

(28) (29)  / 2   = 

 

406

 

 

cool cool cool

 Aug 1, 2022

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