a carpenter has a long wooden plank.The length of the plank is exactly 300cm.the carpenter cuts two shorter planks ,A and B ,from the nearest 10cm,the length of plank A is 50cm ,while the length of the plank B is 110cm .what are the upper and lower bounds of the length of the remaining plank ,after plank A and plank B have been cut out .give your answer in cm

To find the upper and lower bounds of the remaining plank, we need to first determine the bounds for planks A and B, which are cut to the nearest 10 cm.

### Step-by-Step Solution:

1. **Determine the bounds for plank A (50 cm):**
   - Nearest 10 cm means the lower bound is 5 cm less, and the upper bound is 5 cm more than the given length.
   - Lower bound for A: \( 50 \text{ cm} - 5 \text{ cm} = 45 \text{ cm} \)
   - Upper bound for A: \( 50 \text{ cm} + 5 \text{ cm} = 55 \text{ cm} \)

2. **Determine the bounds for plank B (110 cm):**
   - Similarly, the lower bound is 5 cm less, and the upper bound is 5 cm more than the given length.
   - Lower bound for B: \( 110 \text{ cm} - 5 \text{ cm} = 105 \text{ cm} \)
   - Upper bound for B: \( 110 \text{ cm} + 5 \text{ cm} = 115 \text{ cm} \)

3. **Calculate the total length of the remaining plank:**
   - Original plank length: 300 cm

   The remaining length \( L \) is calculated by subtracting the lengths of planks A and B from the original plank.

4. **Calculate the upper bound of the remaining plank:**
   - Subtract the lower bounds of A and B from the original length to get the maximum remaining length.
   - Maximum remaining length: \( 300 \text{ cm} - (45 \text{ cm} + 105 \text{ cm}) = 300 \text{ cm} - 150 \text{ cm} = 150 \text{ cm} \)

5. **Calculate the lower bound of the remaining plank:**
   - Subtract the upper bounds of A and B from the original length to get the minimum remaining length.
   - Minimum remaining length: \( 300 \text{ cm} - (55 \text{ cm} + 115 \text{ cm}) = 300 \text{ cm} - 170 \text{ cm} = 130 \text{ cm} \)

### Answer:
- **Lower bound of the remaining plank:** 130 cm
- **Upper bound of the remaining plank:** 150 cm

Would you like any details or have any questions about this solution?

Here are 5 questions you might want to ask:
1. How do I find the bounds for different measurements?
2. Can you explain how to round numbers to the nearest 10 cm?
3. How does subtracting bounds affect the final result?
4. What if the original plank length was different?
5. How would the solution change if the planks were cut to the nearest 5 cm?

**Tip:** When dealing with measurements and bounds, always consider the precision of the given values and the rules for rounding to ensure accurate results.

Learn how to calculate the upper and lower bounds of the remaining plank length after cutting planks A (50 cm) and B (110 cm) from an original 300 cm plank. This problem involves concepts such as measurement, rounding to the nearest 10 cm, and subtraction. Suitable for students in Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation