19. A ten-foot-long board is cut into three pieces. The second piece is half as long as the first. The third piece is 4 feet longer than the second. How long is the first piece?

Question

19. A ten-foot-long board is cut into three pieces. The second piece is half as long as the first. The third piece is 4 feet longer than the second. How long is the first piece?

A. 1 feet

B. 2 feet

C. 2 feet

D. 3 feet

The answer is given by the teacher to us, but I want to know how to get the correct answer. Thank you.

Answer 1

If the smallest (2nd) piece is x, then just add up the lengths:

2x + x + x+4 = 10

now find x, and you can figure the length needed.

Answer 2

To find the length of the first piece, let's break down the information given in the question.

1. The second piece is half as long as the first piece.
2. The third piece is 4 feet longer than the second piece.

Let's assign a variable to the first piece. Let's call it "x".

1. The second piece is half as long as the first piece. This means the second piece is x/2 feet long.
2. The third piece is 4 feet longer than the second piece. This means the third piece is (x/2) + 4 feet long.

Now, let's add up the lengths of all three pieces:

First piece + Second piece + Third piece = Total length of the board

x + (x/2) + ((x/2) + 4) = 10 feet (since the board length is given as 10 feet)

Now, we can combine like terms to simplify the equation:

2x/2 + 4 = 10

Simplifying further:

x + 4 = 10

Subtracting 4 from both sides:

x = 6

Therefore, the first piece is 6 feet long.

So, the correct answer is D. 3 feet.