Question

A 24-ft pipe must be cut into three pieces. The longest piece will be twice as long as the shirtest piece; and the medium-sized piece will be 4 feet longer than the shortest piece. Find the lenght of each piece of pipe.

Answer 1

To find the lengths of the three pieces of the pipe, we set up equations based on the given information and solve for the variable values. The lengths are 5 feet, 9 feet, and 10 feet.

Step-by-step explanation:

To solve this problem, let's represent the lengths of the three pieces as x, y, and z.

We are given that the longest piece (z) is twice as long as the shortest piece (x), so z = 2x.

We are also given that the medium-sized piece (y) is 4 feet longer than the shortest piece (x), so y = x + 4.

Since the total length of the pipe is 24 feet, we can set up the equation x + y + z = 24 and substitute the known values for y and z to get x + (x + 4) + 2x = 24.

Simplifying the equation, we get 4x + 4 = 24.

Subtracting 4 from both sides gives us 4x = 20. Dividing both sides by 4, we find x = 5.

Therefore, the lengths of the three pieces are x = 5 feet, y = 5 + 4 = 9 feet, and z = 2x = 2(5) = 10 feet.

Answer 2

Writing the length, in feet, of the shortest piece as a variable x, we know that the longest piece is two times the shortest piece, or 2x. Next, we know that the middle sized piece is four feet longer than the shortest piece, or x+4. Therefore, as all the pieces add up to 24 feet, we have x+2x+x+4=4x+4=24. Using the Subtraction Property of Equality and subtracting 4 from both sides, we get 4x=20. Using the Division Property of Equality next, we can divide both sides by 4 to get x=5, making the shortest side, or x, equal to 5

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