How many ordered pairs (x,y) of positive integers satisfy 2x + 5y = 100?

Hi Ann,

Consider the max X that can satisfy (say for now Y=0). So X=50

Similarly max Y=20

so from ordered pair (50,0) and (0,20)

Say you decrease X by 5, then you have to increase Y by 2

So you will have (45,2) (40,4) (35,6)......(5,18) So a total of 9 ordered pairs.

Hope that helps.

All the best.

Regards,

Ashwin (IIT Madras).