Question

A 50-foot piece of siding is cut into three pieces so that the second piece is four times 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 1

The length of the first piece is 5 ft

The length of the second piece is 20 ft

The length of the third piece is 25 ft

Explanation:

Let

x----> the length of the first piece

y ---> the length of the second piece

z ---> the length of the third piece

we know that

`x+y+z=50` -----> equation A

`y=4x` -----> equation B

`z=5x`----> equation C

substitute equation B and equation C in equation A and solve for x

`x+4x+5x=50\\10x=50\\x=5`

Find the value of y

`y=4(5)=20`

Find the value of z

`z=5(5)=25`

therefore

The length of the first piece is 5 ft

The length of the second piece is 20 ft

The length of the third piece is 25 ft