Charlotte Has $22 \frac{1}{3}$ Feet Of Plastic Pipe. She Cuts Off A $4 \frac{1}{2}$-foot Length And Then A $7 \frac{1}{4}$-foot Length. If She Now Needs A 10-foot Piece Of Pipe, Will The Remaining Piece Suffice? If Not, By

Feb 25, 2025 by ADMIN 223 views

**Charlotte's Pipe Puzzle: A Mathematical Conundrum**

Introduction

In this article, we will delve into a mathematical problem involving a piece of plastic pipe. Charlotte has a total of $22 \frac{1}{3}$ feet of plastic pipe, which she needs to cut into smaller pieces to meet her requirements. She cuts off a $4 \frac{1}{2}$ -foot length and then a $7 \frac{1}{4}$ -foot length. Now, she needs a 10-foot piece of pipe, but will the remaining piece suffice? If not, by how much will she fall short?

Calculating the Remaining Length

To determine if the remaining piece of pipe will suffice, we need to calculate the total length of pipe that Charlotte has cut off. We can do this by adding the lengths of the two pieces she cut off.

Length of the First Piece

The length of the first piece is $4 \frac{1}{2}$ feet. To convert this to an improper fraction, we can multiply the whole number part by the denominator and add the numerator:

4 \frac{1}{2} = \frac{(4 \times 2) + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2}

Length of the Second Piece

The length of the second piece is $7 \frac{1}{4}$ feet. To convert this to an improper fraction, we can multiply the whole number part by the denominator and add the numerator:

7 \frac{1}{4} = \frac{(7 \times 4) + 1}{4} = \frac{28 + 1}{4} = \frac{29}{4}

Total Length of Pipe Cut Off

Now that we have the lengths of the two pieces in improper fraction form, we can add them together to find the total length of pipe cut off:

\frac{9}{2} + \frac{29}{4} = \frac{18}{4} + \frac{29}{4} = \frac{47}{4}

Converting to a Mixed Number

To make it easier to work with, we can convert the improper fraction to a mixed number:

\frac{47}{4} = 11 \frac{3}{4}

Remaining Length of Pipe

Now that we know the total length of pipe cut off, we can subtract this from the original length of pipe to find the remaining length:

22 \frac{1}{3} - 11 \frac{3}{4} = \frac{67}{3} - \frac{47}{4}

To subtract these fractions, we need to find a common denominator. The least common multiple of 3 and 4 is 12, so we can rewrite the fractions with a denominator of 12:

\frac{67}{3} = \frac{67 \times 4}{3 \times 4} = \frac{268}{12}

\frac{47}{4} = \frac{47 \times 3}{4 \times 3} = \frac{141}{12}

Now we can subtract the fractions:

\frac{268}{12} - \frac{141}{12} = \frac{127}{12}

Converting to a Mixed Number

To make it easier to work with, we can convert the improper fraction to a mixed number:

\frac{127}{12} = 10 \frac{7}{12}

Will the Remaining Piece Suffice?

Now that we know the remaining length of pipe, we can determine if it will suffice for Charlotte's needs. She needs a 10-foot piece of pipe, but the remaining piece is only $10 \frac{7}{12}$ feet long. Since $10 \frac{7}{12}$ is greater than 10, the remaining piece will suffice.

Conclusion

In this article, we solved a mathematical problem involving a piece of plastic pipe. We calculated the total length of pipe cut off and subtracted this from the original length to find the remaining length. We then determined if the remaining piece would suffice for Charlotte's needs. The remaining piece will suffice, but by how much? To find this out, we can subtract the length of the remaining piece from the length of the piece Charlotte needs:

10 - 10 \frac{7}{12} = - \frac{7}{12}

Since the result is negative, we can conclude that the remaining piece will suffice by $\frac{7}{12}$ feet.

Discussion

This problem involves a variety of mathematical concepts, including fractions, mixed numbers, and subtraction. It also requires the student to think critically and solve a real-world problem. The problem is relevant to the topic of mathematics and requires the student to apply mathematical concepts to a practical situation.

Real-World Applications

This problem has real-world applications in a variety of fields, including construction, engineering, and manufacturing. In these fields, workers often need to cut and measure materials to meet specific requirements. This problem demonstrates the importance of mathematical skills in these fields and provides a practical example of how mathematics is used in real-world situations.

Conclusion

Introduction

In our previous article, we solved a mathematical problem involving a piece of plastic pipe. Charlotte had a total of $22 \frac{1}{3}$ feet of plastic pipe, which she needed to cut into smaller pieces to meet her requirements. She cut off a $4 \frac{1}{2}$ -foot length and then a $7 \frac{1}{4}$ -foot length. Now, she needs a 10-foot piece of pipe, but will the remaining piece suffice? If not, by how much will she fall short?

Q&A

Q: What is the total length of pipe cut off? A: The total length of pipe cut off is $11 \frac{3}{4}$ feet.

Q: How do we calculate the remaining length of pipe? A: To calculate the remaining length of pipe, we subtract the total length of pipe cut off from the original length of pipe.

Q: What is the remaining length of pipe? A: The remaining length of pipe is $10 \frac{7}{12}$ feet.

Q: Will the remaining piece suffice for Charlotte's needs? A: Yes, the remaining piece will suffice for Charlotte's needs.

Q: By how much will the remaining piece suffice? A: The remaining piece will suffice by $\frac{7}{12}$ feet.

Q: What mathematical concepts are involved in this problem? A: This problem involves a variety of mathematical concepts, including fractions, mixed numbers, and subtraction.

Q: What are some real-world applications of this problem? A: This problem has real-world applications in a variety of fields, including construction, engineering, and manufacturing.

Q: Why is it important to solve problems like this? A: Solving problems like this is important because it helps to develop critical thinking and problem-solving skills. It also helps to apply mathematical concepts to real-world situations.

Q: Can you provide more examples of similar problems? A: Yes, here are a few more examples of similar problems:

A carpenter has a total of $15 \frac{1}{2}$ feet of wood to cut into smaller pieces. She cuts off a $3 \frac{1}{4}$ -foot length and then a $6 \frac{1}{2}$ -foot length. Now, she needs a 12-foot piece of wood, but will the remaining piece suffice?
A builder has a total of $20 \frac{3}{4}$ feet of pipe to cut into smaller pieces. He cuts off a $5 \frac{1}{2}$ -foot length and then a $9 \frac{1}{4}$ -foot length. Now, he needs a 15-foot piece of pipe, but will the remaining piece suffice?

Conclusion

In conclusion, this problem involves a variety of mathematical concepts and requires the student to think critically and solve a real-world problem. The problem is relevant to the topic of mathematics and has real-world applications in a variety of fields. We hope that this Q&A article has provided a helpful resource for students and teachers alike.

Additional Resources

For more examples of similar problems, see our previous article on "Charlotte's Pipe Puzzle: A Mathematical Conundrum".
For more information on fractions and mixed numbers, see our article on "Fractions and Mixed Numbers: A Mathematical Guide".
For more information on subtraction, see our article on "Subtraction: A Mathematical Guide".

Discussion

Real-World Applications

This problem has real-world applications in a variety of fields, including:

Construction: In construction, workers often need to cut and measure materials to meet specific requirements. This problem demonstrates the importance of mathematical skills in this field.
Engineering: In engineering, workers often need to design and build structures that meet specific requirements. This problem demonstrates the importance of mathematical skills in this field.
Manufacturing: In manufacturing, workers often need to cut and measure materials to meet specific requirements. This problem demonstrates the importance of mathematical skills in this field.