Answer:
Length 1 = 9 feet
Length 2 = 18 feet
Length 3 = 60 feet
Explanations:
The total length of the rope = 87 feet
Let the length of the first piece be a
Let the length of the second piece be b
Let the length of the third piece be c
The addition of the three pieces will be equal to the total length of the rope
a + b + c = 87....................................(1)
The second piece is two times the length of the first piece:
b = 2a...............................(2)
The third piece is 6 feet more than six times the length of the first piece
c = 6a + 6...................................(3)
Substitute equations (2) and (3) into equation (1)
a + 2a + (6a + 6) = 87
9a + 6 = 87
9a = 87 - 6
9a = 81
a = 81/9
a = 9
Substitute a = 9 into equation (2)
b = 2(9)
b = 18
Substitute a = 9 into equation (3)
c = 6(9) + 6
c = 60
Therefore:
Length 1 = 9 feet
Length 2 = 18 feet
Length 3 = 60 feet