What three numbers have an average of 914?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 914. This means if we add these three numbers together and divide by 3, we should get 914.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 914 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 914 * 3 = x + y + z
- So, the sum of our three numbers should be: 2742
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2742.
Solution 1:
914, 914, 914
Verification:
(914 + 914 + 914) / 3 = 2742 / 3 ≈ 914
This solution is correct!
Solution 2:
914, 914, 914
Verification:
(914 + 914 + 914) / 3 = 2742 / 3 ≈ 914
This solution is correct!
Solution 3:
2573, 50, 119
Verification:
(2573 + 50 + 119) / 3 = 2742 / 3 ≈ 914
This solution is correct!
Solution 4:
1627, 295, 820
Verification:
(1627 + 295 + 820) / 3 = 2742 / 3 ≈ 914
This solution is correct!
Solution 5:
218, 60, 2464
Verification:
(218 + 60 + 2464) / 3 = 2742 / 3 ≈ 914
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 2742 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.