Among five pencils, A, B, C, D and E, the length of D is 10 cm. A is half the length of D but double the length of C. E is 2 cm longer than C. The length of B is equal to the lengths of A and E taken together. Which is the longest pencil?
D
Finding the Longest Pencil Length
This problem involves comparing the lengths of five pencils, A, B, C, D, and E, based on given relationships. We are provided with the length of one pencil and rules relating the others. To find the longest pencil, we must first calculate the length of each pencil.
Step-by-Step Calculation of Pencil Lengths
We start with the known length and use the given relationships to find the lengths of the other pencils one by one.
- Length of Pencil D:
We are given the length of pencil D directly.
\text{Length of D} = 10 \text{ cm}
- Length of Pencil A:
The problem states that A is half the length of D.
\text{Length of A} = \frac{1}{2} \times \text{Length of D}
\text{Length of A} = \frac{1}{2} \times 10 \text{ cm}
\text{Length of A} = 5 \text{ cm}
- Length of Pencil C:
We are told that A is double the length of C. This means C is half the length of A.
\text{Length of C} = \frac{1}{2} \times \text{Length of A}
\text{Length of C} = \frac{1}{2} \times 5 \text{ cm}
\text{Length of C} = 2.5 \text{ cm}
- Length of Pencil E:
The problem states that E is 2 cm longer than C.
\text{Length of E} = \text{Length of C} + 2 \text{ cm}
\text{Length of E} = 2.5 \text{ cm} + 2 \text{ cm}
\text{Length of E} = 4.5 \text{ cm}
- Length of Pencil B:
The length of B is equal to the lengths of A and E taken together (sum of their lengths).
\text{Length of B} = \text{Length of A} + \text{Length of E}
\text{Length of B} = 5 \text{ cm} + 4.5 \text{ cm}
\text{Length of B} = 9.5 \text{ cm}
Comparing Pencil Lengths
Now that we have calculated the length of each pencil, we can compare them to find the longest one.
| Pencil | Length (cm) |
|---|---|
| A | 5.0 |
| B | 9.5 |
| C | 2.5 |
| D | 10.0 |
| E | 4.5 |
Comparing the lengths: 5.0 cm (A), 9.5 cm (B), 2.5 cm (C), 10.0 cm (D), and 4.5 cm (E).
The longest length among these is 10.0 cm, which is the length of pencil D.
Conclusion: Identifying the Longest Pencil
Based on our calculations and comparison, the longest pencil is D.
The lengths are: A = 5 cm, B = 9.5 cm, C = 2.5 cm, D = 10 cm, E = 4.5 cm. The largest value is 10 cm, corresponding to pencil D.
Therefore, the longest pencil is D.
Revision Table: Pencil Lengths Summary
| Pencil | Relationship | Calculated Length (cm) |
|---|---|---|
| D | Given | 10.0 |
| A | Half of D | 5.0 |
| C | Half of A | 2.5 |
| E | 2 cm longer than C | 4.5 |
| B | A and E together | 9.5 |
Additional Information: Solving Comparison Problems
Comparison problems like this require careful reading and step-by-step processing of information. Here are some tips:
- Identify the known quantities first.
- Break down the relationships given in the problem into smaller steps.
- Write down each relationship as an equation or simple statement.
- Solve for unknown quantities one by one, using the results from previous steps.
- Organize your findings, perhaps in a table, to make comparison easier.
- Finally, compare all the calculated values to answer the specific question asked (e.g., longest, shortest, difference, etc.).
Using clear notation and keeping track of units (like cm) is also helpful.
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