Linear Diophantine Equations - Ex 1

[matin-aorosyls.]

Thanks for this video. I really appreciate it. I can now understand where the Linear Diophantine Equation can be apply in real life. I hope you have more videos to be uploaded. God bless you!!

[devondevon]

5x + 2y =30 divide
xo= 2 yo=10
x= xo +bn or x=2 +2n
y= yo -an or y= 10-5n
when n = 0 x = 2 and y= 10 or 2 (50 dollars) + 10 (20 dollars) 100+200=300 dollars
when n= 1, x=4 and y=5 or 4(50 dollars) + 5 (20 dollars ) 200 + 300
n cannot = 3 hence 2+ 2n 2+ 6 = 8 or x would =8 and 8 x 50= 400 dollars exceeding 300 dollars.
so in his pocket he has to have even numbers of 50 dollars such as 2, 50 dollars or 4, 50 dollars. he cant have 6, 50 dollars (6 x 50 =300) since it said that he has some 20 dollars dollar.
so he either has 2, 50 dollars hence 10, 20 dollars in his pocket or he has 4, 50 dollars hence 5, 20 dollars. the general formula (answer) is x=2 + 2n where x is the number of 50 dollars and n is an integer and (answer)y=10-5n where y is the number of 20 dollars and n is an integer. n is range from 0 to 1 (integers) n is either 0 or 1 . here one equation has a plus (x= 2 + 2n) and the other a minus (y= 10-5n) this is because as one increase the other has to decrease or has one decrease as to increase, so when 50 dollar increase, then 20 dollars has to decrease, ie the more 50 dollar he has the less 20 dollars,
and the more 20 dollars the less 50 dollars

[devondevon]

5:59 t can be 2 only and only if Robert had no 20 dollars note(so 6, 50 dollars or 300 dollars and no 20 dollars), so 2 +2(2)= 6 x 50= 300 dollars
t also can only and only be -1 if he has no 50 dollars note, 10+ 5= 15 x 20= 300 dollars. If he had both 50 and 20 dollar bill then t, CANNOT BE -1 AND 2 BUT range from 0 to 1, or 0 and 1, and in this case he would need to have an even number of 50 dollar bill such as 2, 50 dollar bill or 4, 50, dollar bill and 10, 20 bill or 5, 20 dollar bill respectively, IF THE TOTAL BILL EQUALS 300 dollars of 50 and 20 dollar bills