We can simplify the inequality first:
Dividing by 4,
x + 2y < 5
Remember the problem says positive integers. Therefore, we can count the limited number of possibilties:
(1, 1)
(2, 1)
(1, 2) doesn't work because 5 is not smaller than 5.
That's it, because if any of the numbers were larger, x + 2y would be bigger than 5.
Thus the number of ordered pairs of positive integers that satisfy the inequality is 2.
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ShockFish
