A ribbon 106 inches long is cut into three pieces. The middle-sized piece is 4 inches longern than twice the shortest piece. the longest piece is 3 times as long as the shortest piece. how long is the shortest piece?
S+L+M=106
S+3S+(2S+4)=106
then solve for S, and L is 3 times that.
To find the length of the shortest piece, let's assign a variable to represent it. Let's call the length of the shortest piece "x" inches.
According to the information given, the middle-sized piece is 4 inches longer than twice the shortest piece. So, the middle-sized piece is 2x + 4 inches long.
The longest piece is three times as long as the shortest piece. Therefore, the longest piece is 3x inches long.
Since the total length of the ribbon is 106 inches and it is cut into three pieces, we can write an equation:
x + (2x + 4) + 3x = 106
Now, let's solve for x:
6x + 4 = 106
6x = 102
x = 17
Therefore, the shortest piece is 17 inches long.