How many ordered pairs (x,y) of positive integers satisfy the inequality 4x+5y < 120?
+128475 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
