To determine how many jelly beans are in the 2-liter jar based on the given data, we need to break down the problem step by step.

Step 1: Extract useful information

• Total weight (including jar and jelly beans): 1,150 grams
• Weight of the jar: 440 grams
• Sample size of jelly beans: 20 jelly beans
• Weights of sample sizes (for 20 jelly beans):
  • Sample 1: 22.0 grams
  • Sample 2: 22.2 grams
  • Sample 3: 22.3 grams

Step 2: Calculate the average weight of one jelly bean

We can use the sample data to estimate the average weight of one jelly bean by first calculating the average weight of 20 jelly beans.

Average weight of 20 jelly beans:

$\text{Average weight} = \frac{22.0 + 22.2 + 22.3}{3} = \frac{66.5}{3} = 22.17 \, \text{grams}$

So, the average weight of 20 jelly beans is approximately 22.17 grams.

Weight of 1 jelly bean:

To find the weight of one jelly bean, we divide the average weight of 20 jelly beans by 20: $\text{Weight of 1 jelly bean} = \frac{22.17}{20} = 1.1085 \, \text{grams}$ So, the average weight of one jelly bean is approximately 1.11 grams.

Step 3: Find the weight of just the jelly beans in the jar

The total weight provided includes both the jar and the jelly beans. To find the weight of just the jelly beans: $\text{Weight of jelly beans} = \text{Total weight} - \text{Weight of jar} = 1,150 \, \text{g} - 440 \, \text{g} = 710 \, \text{grams}$

Step 4: Calculate the number of jelly beans in the jar

Now, to find the total number of jelly beans, we divide the weight of the jelly beans in the jar by the average weight of one jelly bean: $\text{Number of jelly beans} = \frac{710}{1.11} \approx 639.64$

Since the number of jelly beans must be a whole number, we round this to 640 jelly beans.

Final Answer:

There are approximately 640 jelly beans in the 2-liter jar.

Would you like me to provide further details on any part of the process or go through additional calculations?

Here are 5 related questions that might interest you:

1. How does the average weight of jelly beans vary with different brands?
2. What is the significance of taking multiple sample measurements for accuracy?
3. How would the volume of the jar affect the number of jelly beans if we had that information?
4. Could the density of jelly beans affect the packing efficiency in the jar?
5. How would errors in measurement affect the final jelly bean count?

Tip: Always take multiple samples when estimating an average to reduce error and increase accuracy in real-life measurements.