A pipe is 42 inches long. It is to be cut into three pieces such that the longest is four times as long as the shortest and the middle-size piece is six inches longer than the shortest. How long is the middle-sized piece?
Let x = the shortest.
4x + x + x + 6 = 42
6x = 42 - 6
6x = 36
x = 6
The middle size piece is 12 inches long.
To find the length of the middle-sized piece, we first need to represent the relationships between the lengths of the three pieces mathematically. Let's assume that the length of the shortest piece is "x" inches.
According to the given information:
- The longest piece is four times as long as the shortest piece, so its length is 4x inches.
- The middle-sized piece is six inches longer than the shortest piece, so its length is (x + 6) inches.
Since we know that the sum of the three pieces is equal to the total length of the pipe, we can create an equation:
x + 4x + (x + 6) = 42
Now, let's simplify the equation and solve for x:
6x + 6 = 42
6x = 36
x = 6
So, the length of the shortest piece is 6 inches. Now, we can find the length of the middle-sized piece:
Length of middle-sized piece = x + 6 = 6 + 6 = 12 inches.
Therefore, the middle-sized piece is 12 inches long.