the grocer buys 620kg of onions , correct to the nearest 20kg. he packs them into bags each bag containing 5kg of onions , correct to the nearest 1kg . calculate the upper bound  for the number of bags of onions that he packs

To calculate the upper bound for the number of bags of onions that the grocer can pack, we need to consider the upper bounds of both the weight of onions purchased and the weight that each bag can hold.

### Step 1: Find the Upper Bound of the Total Weight of Onions
The grocer buys 620 kg of onions, correct to the nearest 20 kg.

- The upper bound for the total weight is calculated by adding half of the rounding unit to the rounded value:
  
  \[
  \text{Upper bound of total weight} = 620 \, \text{kg} + \frac{20 \, \text{kg}}{2} = 620 \, \text{kg} + 10 \, \text{kg} = 630 \, \text{kg}
  \]

### Step 2: Find the Lower Bound of the Weight per Bag
Each bag contains 5 kg of onions, correct to the nearest 1 kg.

- The lower bound for the weight of each bag is calculated by subtracting half of the rounding unit from the rounded value:
  
  \[
  \text{Lower bound of weight per bag} = 5 \, \text{kg} - \frac{1 \, \text{kg}}{2} = 5 \, \text{kg} - 0.5 \, \text{kg} = 4.5 \, \text{kg}
  \]

### Step 3: Calculate the Upper Bound for the Number of Bags
To find the upper bound of the number of bags, divide the upper bound of the total weight by the lower bound of the weight per bag:

\[
\text{Upper bound for the number of bags} = \frac{630 \, \text{kg}}{4.5 \, \text{kg/bag}} = 140 \, \text{bags}
\]

Thus, the upper bound for the number of bags that the grocer can pack is **140 bags**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you calculate the lower bound for the number of bags?
2. What if the total weight was rounded to the nearest 10 kg instead of 20 kg?
3. How does rounding affect the accuracy of calculations in practical scenarios like this?
4. Can you find the exact number of bags if the exact total weight and exact bag capacity were known?
5. How would this problem change if each bag was packed with a variable weight?

**Tip:** When working with upper and lower bounds, always pay attention to the units and how rounding affects them.

Learn how to calculate the upper bound for the number of bags of onions a grocer can pack, given rounded weights and bag capacities. This problem involves rounding, division, and understanding upper and lower bounds in practical scenarios. 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