Q:

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

Accepted Solution

A:
Answer:The length of the first piece is 5 ftThe length of the second piece is 20 ftThe length of the third piece is 25 ftStep-by-step explanation:Letx----> the length of the first piecey ---> the length of the second piecez ---> the length of the third piecewe know that[tex]x+y+z=50[/tex] -----> equation A[tex]y=4x[/tex] -----> equation B[tex]z=5x[/tex]----> equation Csubstitute equation B and equation C in equation A and solve for x[tex]x+4x+5x=50\\10x=50\\x=5[/tex]Find the value of y[tex]y=4(5)=20[/tex]Find the value of z[tex]z=5(5)=25[/tex]thereforeThe length of the first piece is 5 ftThe length of the second piece is 20 ftThe length of the third piece is 25 ft