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