Question

Kiki has a piece of string that she cuts into smaller pieces. This line plot shows the lengths of the pieces. Raj has a piece of string that is 12 as long as Kiki's third-longest piece. (Note: The problem says third-longest piece, not third-longest length.)

How long is Raj's piece of string?

Enter your answer as a mixed number in simplest form by filling in the boxes.

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in.
Line plot titled Pieces of String. The number line is labeled Length in inches and goes from 4 and 1 fourth to 5 and 3 fourths by fourths. There are 2 marks above 4 and 1 fourth, 3 marks above 4 and 1 half, 2 marks above 4 and 3 fourths, 2 marks above 5, 4 marks above 5 and 1 fourth, 1 mark above 5 and 1 half, and 2 marks above 5 and 3 fourths.

Answer 1

To determine the length of Raj's piece of string, we need to find Kiki's third-longest piece of string from the given line plot.

First, let's identify the lengths of string pieces present in the line plot:

- 4 and 1/4 inches (2 pieces)
- 4 and 1/2 inches (3 pieces)
- 4 and 3/4 inches (2 pieces)
- 5 inches (2 pieces)
- 5 and 1/4 inches (4 pieces)
- 5 and 1/2 inches (1 piece)
- 5 and 3/4 inches (2 pieces)

Now we will arrange these lengths in order from longest to shortest:

1. 5 and 3/4 inches
2. 5 and 1/2 inches
3. 5 and 1/4 inches
4. 5 inches
5. 4 and 3/4 inches
6. 4 and 1/2 inches
7. 4 and 1/4 inches

The third-longest piece is **5 and 1/4 inches**.

Next, we calculate how long Raj's piece of string is. According to the problem, Raj's piece is 12 times the length of Kiki's third-longest piece:

\[
Raj's \ piece \ length = 12 \times (5 + \frac{1}{4}) = 12 \times \frac{21}{4}
\]

Calculating that:

\[
Raj's \ piece \ length = \frac{12 \times 21}{4} = \frac{252}{4} = 63
\]

Thus, Raj's piece of string is **63 inches** long.

Since the problem asks for the answer in mixed number form, we can convert **63** into a mixed number:

\[
63 = 63 \frac{0}{1}
\]

So, the final answer is:

**63** in mixed number form is:

\[
63 \, \frac{0}{1}
\]

**Answer: 63 0**