What three numbers have an average of 731?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 731. This means if we add these three numbers together and divide by 3, we should get 731.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 731 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 731 * 3 = x + y + z
- So, the sum of our three numbers should be: 2193
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2193.
Solution 1:
731, 731, 731
Verification:
(731 + 731 + 731) / 3 = 2193 / 3 ≈ 731
This solution is correct!
Solution 2:
731, 731, 731
Verification:
(731 + 731 + 731) / 3 = 2193 / 3 ≈ 731
This solution is correct!
Solution 3:
1413, 269, 511
Verification:
(1413 + 269 + 511) / 3 = 2193 / 3 ≈ 731
This solution is correct!
Solution 4:
2025, 123, 45
Verification:
(2025 + 123 + 45) / 3 = 2193 / 3 ≈ 731
This solution is correct!
Solution 5:
17, 1021, 1155
Verification:
(17 + 1021 + 1155) / 3 = 2193 / 3 ≈ 731
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 2193 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.