A rope 116 inches is cut into three pieces.The middle-sized piece is 10 inches shorter than twice the shortest piece.The longest piece is 5/3 as long as the shortest piece.What is the length of the shortest piece?
if the pieces are a < b < c,
a+b+c = 116
b = 2a - 10
c = 5/3 a
the pieces are 27,44,45
To find the length of the shortest piece, let's assign a variable to represent its length. Let's call it "x".
According to the information given, we can find the lengths of the other two pieces in terms of this variable.
1. The middle-sized piece is 10 inches shorter than twice the shortest piece, meaning it is equal to (2x - 10) inches.
2. The longest piece is 5/3 as long as the shortest piece, meaning it is equal to (5/3)x.
Now, we can set up an equation to solve for the length of the shortest piece. The sum of all three pieces must equal the total length of the rope:
x + (2x - 10) + (5/3)x = 116
Simplifying the equation:
x + 2x - 10 + (5/3)x = 116
Multiplying throughout by 3 to get rid of the fraction:
3x + 6x - 30 + 5x = 348
14x - 30 = 348
Adding 30 to both sides:
14x = 378
Dividing by 14:
x = 27
Therefore, the length of the shortest piece is 27 inches.