Hi,

I have been working to solve this question-"Suppose,we have two strings A and B of lengths 5 cm and 6 cm respectively.And,we have another piece of string C whose length is 4 cm.Now,we have to make the strings A and B equal in length by cutting the string C and adding it to A and B such that string C is completely used.Find what length of strings should be added to A and B ?"

I solved this question in this way,

Let the length of string added to A be "x" and the length of string added to B be "y".

Then,5+x=6+y

=> x-y=1......(i)

And,x+y=4.....(ii)

On adding (i) and (ii) we get,

=>x=5/2=2.5 and y = 1.5

So,i must say that i have gone on to solve this question blindly(without know exactly what really happens when i add those two

equation (i) & (ii)).

Now,i want to know what is really going on when i combine(add) those two equations?Why do i get a reasonable value of 'x' when i add them?Why does combining those equations gives me answer of what length should be added? CAN ANYONE HERE GIVE ME AN INTUITIVE EXPLANATION OF WHAT IS REALLY HAPPENING?*I want to know why adding those two equations can precisely divide 4 cm into such two parts which when added to A and B makes them equal(A=B)?*

I have another doubt,

After solving the question i get these answers- (2.5,1.5).

now what i want to know is that why can't there another set of number exist (X,Y) such that X+Y=4 and 5+X=6+Y ? (Why can't another set of number exist which can satisfy the demands of the question ?)

I will be thankful for help!

Note:I am a high school student and English is my second language.

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