What three numbers have an average of 830?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 830. This means if we add these three numbers together and divide by 3, we should get 830.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 830 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 830 * 3 = x + y + z
- So, the sum of our three numbers should be: 2490
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2490.
Solution 1:
830, 830, 830
Verification:
(830 + 830 + 830) / 3 = 2490 / 3 ≈ 830
This solution is correct!
Solution 2:
830, 830, 830
Verification:
(830 + 830 + 830) / 3 = 2490 / 3 ≈ 830
This solution is correct!
Solution 3:
498, 1920, 72
Verification:
(498 + 1920 + 72) / 3 = 2490 / 3 ≈ 830
This solution is correct!
Solution 4:
1880, 474, 136
Verification:
(1880 + 474 + 136) / 3 = 2490 / 3 ≈ 830
This solution is correct!
Solution 5:
2180, 307, 3
Verification:
(2180 + 307 + 3) / 3 = 2490 / 3 ≈ 830
This solution is correct!
Explanation:
As you can see, there are many possible solutions. We can find more by:
- Choosing any two numbers
- Subtracting their sum from 2490 to get the third number
Remember:
- The numbers don't have to be whole numbers.
- They can even be negative (although that might not make sense in some real-world contexts).
- The order of the numbers doesn't matter for the average.