A 24 -foot piece of siding is cut into three pieces so that the second piece is twice as long as the first piece and the third piece is five times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.

Answer: first piece = 3 feet

Second piece = 6 feet

Third piece = 15 feet.

Step-by-step explanation:

The total length of the siding is 24 feet.

It is cut into three pieces so that the second piece is twice as long as the first piece. If x represents the length of the first piece, then the length of the second piece is 2x.

If the third piece is five times as long as the first piece, then the length of the third piece would be

5x. Therefore,

x + 2x + 5x = 24

8x = 24

x = 24/8

x = 3 feet

Length of the second piece = 2 * 3 = 6 feet.

Length of the third piece = 5 * 3 =

15 feet.

Let x be the first piece, y the 2nd, Z the 3rd

You know all of the pieces together make 24 thus,

24 = x + y + z

The second piece is 2 times longer than the 1st so,

y = 2x

The 3rd is 5 times longer

z = 5x

Replace them in the equation of the beginning

24 = x + 2x + 5x

24 = 8x

x = 3 (First piece)

y = 6 (Second Piece)

z = 15 (Third Piece)