Hi there!
In order to solve for this length, we need to make a series of equations based on what is given in the question. First, we need to make a set of variables.
A=1st piece
B=2nd piece
C=3rd piece
A+B+C=150 (a 150-inch long ribbon is cut into three pieces; this means the 3 pieces equal 150 inches when added together)
A=2B (the 1st piece is 2 times the second piece)
C=3B (the 3rd piece is 3 times the second piece)
We can sub A and C into the first equation, allowing us to solve for B. Then, we can sub B into the equation for C (the longest piece) to find the length of C.
A+B+C=150
2B+B+3B=150
6B=150
B=150/6
B=25
C=3B
C=3×25
C=75
Therefore the largest piece of ribbon is 75 inches long
Hope this helps!