Calculate Total from Average: Finding Sum of 4 Pens in 5 Bags

Q: Why do I multiply the average by the number of bags?

The average tells you how many pens are in each bag on average. Since Roni has 5 bags, you need to multiply 4 × 5 to find the total across all bags!

Q: What if the bags don't all have exactly 4 pens?

That's okay! An average means some bags might have more than 4 pens and others might have fewer. The total is still $ 4 \times 5 = 20 $ pens.

Q: How can I check if 20 is the right answer?

Divide the total by the number of bags: $ 20 \div 5 = 4 $. This should equal the original average, which it does!

Q: Is this the same as finding the sum from mean?

Yes! Average and mean are the same thing. The formula Total = Mean × Count works for any averaging problem.

Average Calculations with Total Sum Finding

Roni has 5 bags.

If the average number of pens in each bag is 4, then how many pens in total does Roni have?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Roni has 5 bags.

If the average number of pens in each bag is 4, then how many pens in total does Roni have?

Step-by-step solution

To solve this problem, we'll apply the concept of the average:

Step 1: Identify the given information. The average number of pens in each bag is $4$ and there are $5$ bags.
Step 2: Use the formula for the total sum based on the average: $\text{Total Sum} = \text{Average} \times \text{Number of Terms}$ .
Step 3: Substitute the given values into the formula: $\text{Total Sum} = 4 \times 5$ .
Step 4: Perform the multiplication: $4 \times 5 = 20$ .

Therefore, the total number of pens Roni has is $20$ .

Final Answer

$20$

Key Points to Remember

Essential concepts to master this topic

Formula: Total Sum = Average × Number of Items
Technique: Multiply 4 pens/bag × 5 bags = 20 total pens
Check: Divide total by number of bags: 20 ÷ 5 = 4 average ✓

Common Mistakes

Avoid these frequent errors

Confusing average with total
Don't think the average IS the total number of pens = only 4 pens total! This ignores that the average represents ALL bags combined. Always multiply the average by the number of groups to find the total.

Practice Quiz

Test your knowledge with interactive questions

Calculate the average of $$ 10 $$ and $$ 12 $$ .

FAQ

Everything you need to know about this question

Why do I multiply the average by the number of bags?

The average tells you how many pens are in each bag on average. Since Roni has 5 bags, you need to multiply 4 × 5 to find the total across all bags!

What if the bags don't all have exactly 4 pens?

That's okay! An average means some bags might have more than 4 pens and others might have fewer. The total is still $4 \times 5 = 20$ pens.

How can I check if 20 is the right answer?

Divide the total by the number of bags: $20 \div 5 = 4$ . This should equal the original average, which it does!

Is this the same as finding the sum from mean?

Yes! Average and mean are the same thing. The formula Total = Mean × Count works for any averaging problem.

What if I accidentally add 4 + 5 instead?

Adding gives you 9, which doesn't make sense here. You're finding how many pens are in multiple bags, so you need to multiply, not add!

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