If a 25 inch rope is cut into three pieces such that the middle sized piece is 1 inch longer thatn the short piece and the longest piece is twice as long as the short piece.

Let's see if we can figure this out. Start by listing the information in a way that let's you use math on it. We'll do that by using variables for each of the 3 sides

x=shortest

y=middle

z=longest

we know the total length is 25in so:

x + y + z = 25in

We also know some more stuff like:

y = x + 1in

z = 2x

Ok that's good now we can just replace y and z with those last bits of info and get

x + [x+1in] + 2x = 25in

x + x + 2x = 24in

4x = 24in

x = 6in

Now we now the short side just plug that info into the other equations

y = x + 1in = 6in + 1in

y = 7 in

z = 2x = 2 * 6in

z= 12in

so the short side is 6in, the middle is 7in, the longest is 12in