What three numbers have an average of 846?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 846. This means if we add these three numbers together and divide by 3, we should get 846.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 846 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 846 * 3 = x + y + z
- So, the sum of our three numbers should be: 2538
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2538.
Solution 1:
846, 846, 846
Verification:
(846 + 846 + 846) / 3 = 2538 / 3 ≈ 846
This solution is correct!
Solution 2:
846, 846, 846
Verification:
(846 + 846 + 846) / 3 = 2538 / 3 ≈ 846
This solution is correct!
Solution 3:
470, 1313, 755
Verification:
(470 + 1313 + 755) / 3 = 2538 / 3 ≈ 846
This solution is correct!
Solution 4:
91, 1037, 1410
Verification:
(91 + 1037 + 1410) / 3 = 2538 / 3 ≈ 846
This solution is correct!
Solution 5:
2433, 46, 59
Verification:
(2433 + 46 + 59) / 3 = 2538 / 3 ≈ 846
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 2538 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.