A150-inch-long ribbon is cut into 3 pieces. the 1st piece is twice as long as the 2nd piece. the 3rd piece is three times as long as the 2nd piece. what is the length of the largest piece of ribbon?

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!