SOLUTION: Find the total number of pairs of (x,y) satisfying the equation 3x+5y=100, x and y are positive integers

Question 979180: Find the total number of pairs of (x,y) satisfying the equation 3x+5y=100, x and y are positive integers

Answer by anand429(138) (Show Source): You can put this solution on YOUR website!
3x + 5y =100
=> y = (100-3x)/5
Since x and y are both positive integer,
so x has to lie between 1 and 33 -------------(condition 1)
Now y is a integer, hence (100-3x) must be a multiple of 5
For(100-3x) to be a multiple of 5, 3x also has to be multiple of 5
which is possible only when x is a multiple of 5 -----(condition 2)
So, possible values of x meeting conditions 1 and 2 are:-
x= 5,10,15,20,25,30
Hence , all possible required pairs of x and y are:-
5,17
10,14
15,11
20,8
25,5
30,2
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