A 20-inch board is to be cut into three pieces so that the second piece is 4 times as long as the first piece and the third piece is 5 times as long as the first piece. If [tex]x[/tex] represents the length of the first piece, find the lengths of all three pieces.
First piece: [tex]x[/tex]
Second piece: [tex]4x[/tex]
Third piece: [tex]5x[/tex]
Answer (3)
First piece = one time Second piece = 4 times Third piece = 5 times
Total board before cutting: 10 times = 20 inches.
Divide each side by 10: 1 time = 2 inches
First piece (x) = 1 time = 2 inches Second piece = 4 times = 8 inches Third piece = 5 times= 10 inches .
Check: Total length of all 3 pieces = (2 + 8 + 10) = 20 inches yay!
1st piece - x 2nd piece - 4x 3rd piece - 5x
x + 4 x + 5 x = 20 10 x = 20 x = 2 4 x = 4 ⋅ 2 = 8 5 x = 5 ⋅ 2 = 10
1st piece - 2 in 2nd piece - 8 in 3rd piece - 10 in
The first piece is 2 inches, the second piece is 8 inches, and the third piece is 10 inches. These lengths collectively total 20 inches. The second piece is four times the length of the first piece, and the third piece is five times the length of the first piece.
;
