Question

A ​27-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first​ piece, and the third piece is three inches more than three times the length of the first piece. Find the lengths of the pieces.

Answer 1

Let's assume the length of the first piece is "x" inches.

According to the given information:
- The second piece is twice as long as the first piece, so its length is 2x inches.
- The third piece is three inches more than three times the length of the first piece, so its length is 3x + 3 inches.

Since the total length of the steel is 27 inches, the sum of the lengths of the three pieces should equal 27 inches:

x + 2x + (3x + 3) = 27

Now, we can solve this equation to find the value of x:

6x + 3 = 27
6x = 27 - 3
6x = 24
x = 24 / 6
x = 4

The length of the first piece is 4 inches.

Using this value, we can find the lengths of the second and third pieces:

Second piece: 2x = 2 * 4 = 8 inches
Third piece: 3x + 3 = 3 * 4 + 3 = 15 inches

So, the lengths of the three pieces are:
First piece: 4 inches
Second piece: 8 inches
Third piece: 15 inches