A 180 ft long board is cut into 3 pieces. The second piece of board is twice as long as the first. The third piece of board is six times as long as the first.
What is the length of the first piece of the board
A) 20 ft
B) 40 ft
C) 60 ft
D) 120 ft
I answered one for you. Now it's your turn. I'll be glad to check your answer.
20ft
To solve this problem, we can use algebra. Let's assume the length of the first piece of the board is 'x'.
Given that the second piece is twice as long as the first, we can say that its length is 2x.
Similarly, the third piece is six times as long as the first, so its length is 6x.
We know that the total length of the board is 180 ft, so we can write the equation:
x + 2x + 6x = 180
Combining like terms, we get:
9x = 180
Dividing both sides of the equation by 9, we find:
x = 20
Therefore, the length of the first piece of the board is 20 ft.
So, the answer is option A) 20 ft.