How many pairs of Positive Integers x and y satisfy the equation 5x + 3y =100

Question

Please help this question is a killer.

Answer 1

5x + 3y = 100

 

        3y = -5x + 100

 

         y = (-5/3)x + (100/3)

 

y intercept:  (0, 100/3)

 

x intercept:  (20, 0)

 

When x and y are both positive, the graph lies in quadrant 1 with x-values between 0 and 20 and y-values between 0 and 33.3333.  

 

             5x = -3y + 100     So, x = 20 - (3/5)y

 

                                             if y = 5, then x = 17

                                             if y = 10, then x = 14

                                             if y = 15, then x = 11

                                             if y = 20, then x = 8

                                             if y = 25, then x = 5

                                             if y = 30 then x = 2

 

So, there are 6 ordered pairs of positive integers (x,y) where 5x+3y = 100.

 

 

Answer 2

5x + 3y = 100

3y =100 - 5x

y = (100 - 5x)/3

 

      x           y   

     0      33 1/3

     1      31 2/3

     2      30

 

There are an infinite number of ordered pairs that will work.