Question

Roberto cut a strip of paper that was 16.5 centimeters long into three pieces.
The largest piece was 0.5 centimeter longer than the second largest piece. The second largest piece was 0.5 centimeter longer than the smallest piece. What is the length of the largest piece of paper?
A. 5.5 cm
B. 6 cm
C. 6.25 cm
D. 6.5 cm

Answer 1

Let's denote the lengths of the three pieces as follows:

- Let \( x \) be the length of the smallest piece.
- The second largest piece will then be \( x + 0.5 \) cm.
- The largest piece will be \( (x + 0.5) + 0.5 = x + 1 \) cm.

The total length of the three pieces is given as 16.5 cm. Therefore, we can set up the equation:

\[
x + (x + 0.5) + (x + 1) = 16.5
\]

Combining like terms:

\[
3x + 1.5 = 16.5
\]

Subtracting 1.5 from both sides:

\[
3x = 16.5 - 1.5 = 15
\]

Dividing both sides by 3:

\[
x = \frac{15}{3} = 5
\]

Now that we have \( x \), we can find the lengths of the pieces:

- Smallest piece: \( x = 5 \) cm
- Second largest piece: \( x + 0.5 = 5 + 0.5 = 5.5 \) cm
- Largest piece: \( x + 1 = 5 + 1 = 6 \) cm

Thus, the length of the largest piece of paper is

\[
\boxed{6 \text{ cm}}
\]

This corresponds to answer choice B.