Twine into three pieces, lets call them x, y and z
The second piece is 7 times as long as the first piece
7x = y
The third piece is 5 feet longer than the first piece
x + 5 = z
The total length of twine is 320 feet
x + y + z = 320
This is a simultaneous equation.
My goal is to make the final equation in terms of x i.e. 5.5x = 320
I choose the final equation because it is the only equation which has a value in it.
We will substitute the first and second equation into the third equation.
7x = y , x + 5 = z
x + y + z = 320
x + (7x) + (x+5) = 320
9x + 5 = 320
9x = 315
x = 35
Now that we know x, we can substitute it into the first and second equation to find x and y
7x = y => 7(35) = y => 245 = y
x + 5 = z => (35) + 5 = z => 40 = z
In summary
>The first piece, x, is 35 feet long
>The second piece, y, is 245 feet long
>The third piece, z, is 40 feet log