296,725 views
13 votes
13 votes
A 87-foot length of rope is cut into 3 pieces, so that the second piece is two times the length of the first piece, and the third piece is 6 feet more than six times the length of the first piece. Find the length of each piece. length 1 = feet length 2 = feet length 3 = feet Question Help: Message instructor Submit Question

User Zitix
by
2.4k points

1 Answer

7 votes
7 votes
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

User Kjeld Schmidt
by
3.0k points