I need help ASAP will give brainliest Divide 1000 into two parts such that one part is a multiple of 47 and the other is a multiple of 19 ( Show me your working)​

x = 14, y = 18

Explanation:

19x + 47y = 1000

^^^This is a Diophantine equation.  

gcd (47,19) = 1  

1 is divisible by 1000 -> Euclidean Algorithm.  

47=2 (19)+9  

19=2 (9)+1 (1 is the gcd )  

1=19–2 (9)=19–2 [47–2 (19)=5 (19)-2 (47)

5000 (19)-2000 (47)=1000.  

1000 =(5000–47)19 -(2000–19)47  

=(5000–106×47)19 - (2000–106×19)47  

=18×19-(-14)47  

=342 +658

x = 18, y = 14

check: 14 x 47 = 658, 18 x 19 = 342, 658 + 342 = 1000.

So the two numbers are 658 and 342.

Explanation:

Let the parts be x and y.

47x + 19y = 1000

dealing with two digit number between 10-20

by inspection 14 and 19 randomly picks

47*14 + 18*19 = 1000

658 + 342 = 1000

So the two numbers are 658 and 342. Answer.