What three numbers have an average of 794?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 794. This means if we add these three numbers together and divide by 3, we should get 794.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 794 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 794 * 3 = x + y + z
- So, the sum of our three numbers should be: 2382
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2382.
Solution 1:
794, 794, 794
Verification:
(794 + 794 + 794) / 3 = 2382 / 3 ≈ 794
This solution is correct!
Solution 2:
794, 794, 794
Verification:
(794 + 794 + 794) / 3 = 2382 / 3 ≈ 794
This solution is correct!
Solution 3:
456, 68, 1858
Verification:
(456 + 68 + 1858) / 3 = 2382 / 3 ≈ 794
This solution is correct!
Solution 4:
1905, 157, 320
Verification:
(1905 + 157 + 320) / 3 = 2382 / 3 ≈ 794
This solution is correct!
Solution 5:
1340, 1035, 7
Verification:
(1340 + 1035 + 7) / 3 = 2382 / 3 ≈ 794
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 2382 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.