What three numbers have an average of 916?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 916. This means if we add these three numbers together and divide by 3, we should get 916.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 916 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 916 * 3 = x + y + z
- So, the sum of our three numbers should be: 2748
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2748.
Solution 1:
916, 916, 916
Verification:
(916 + 916 + 916) / 3 = 2748 / 3 ≈ 916
This solution is correct!
Solution 2:
916, 916, 916
Verification:
(916 + 916 + 916) / 3 = 2748 / 3 ≈ 916
This solution is correct!
Solution 3:
1726, 995, 27
Verification:
(1726 + 995 + 27) / 3 = 2748 / 3 ≈ 916
This solution is correct!
Solution 4:
2676, 16, 56
Verification:
(2676 + 16 + 56) / 3 = 2748 / 3 ≈ 916
This solution is correct!
Solution 5:
2399, 185, 164
Verification:
(2399 + 185 + 164) / 3 = 2748 / 3 ≈ 916
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 2748 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.