Let the length of the first piece be "x", second piece be "y" and third piece be "z".
Total length is 234 inches, so we can write:
[tex]x+y+z=234[/tex]Also,
• Second piece is 4 times the first piece, ,we can write:
[tex]y=4x[/tex]• Third piece is 8 times the first piece, ,we can write:
[tex]z=8x[/tex]Substituting these 2 equations into the first equation, we will have an equation in x. Then we solve for x. Shown below:
[tex]\begin{gathered} x+y+z=234 \\ x+4x+8x=234 \\ 13x=234 \\ x=18 \end{gathered}[/tex]Consequently, we can find y and z >>>>
y = 4x
y = 4(18)
y = 72
and
z = 8x
z = 8(18)
z = 144
Answer
First Piece = 18 inches
Second Piece = 72 inches
Third Piece = 144 inches