I am asking this question for concept clarification :-
How many integral solutions are there to a+b+c=18 when a 1 , b 2 , c 3 ?
Solution: Let u 0, v 0, w 0, then
a u+1 , b v+2 , c w+3,
Therefore, a + b + c = 18
or u+1 + v+2 + w+3 = 18
or u + v + w =12. From there we solve as usual.
My question is why are we using: Let u 0, v 0, w 0, then
a u+1 , b v+2 , c w+3
Is it to convert each variable i.e a,b and c to one unit each ( since a,b ,c are unequal) or for any other reason ? What is the underlying logic ? Please advise on the above.
Thanks in advance !