What three numbers have an average of 847?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 847. This means if we add these three numbers together and divide by 3, we should get 847.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 847 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 847 * 3 = x + y + z
- So, the sum of our three numbers should be: 2541
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2541.
Solution 1:
847, 847, 847
Verification:
(847 + 847 + 847) / 3 = 2541 / 3 ≈ 847
This solution is correct!
Solution 2:
847, 847, 847
Verification:
(847 + 847 + 847) / 3 = 2541 / 3 ≈ 847
This solution is correct!
Solution 3:
2305, 94, 142
Verification:
(2305 + 94 + 142) / 3 = 2541 / 3 ≈ 847
This solution is correct!
Solution 4:
1609, 841, 91
Verification:
(1609 + 841 + 91) / 3 = 2541 / 3 ≈ 847
This solution is correct!
Solution 5:
360, 2012, 169
Verification:
(360 + 2012 + 169) / 3 = 2541 / 3 ≈ 847
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 2541 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.