What three numbers have an average of 920?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 920. This means if we add these three numbers together and divide by 3, we should get 920.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 920 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 920 * 3 = x + y + z
- So, the sum of our three numbers should be: 2760
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2760.
Solution 1:
920, 920, 920
Verification:
(920 + 920 + 920) / 3 = 2760 / 3 ≈ 920
This solution is correct!
Solution 2:
920, 920, 920
Verification:
(920 + 920 + 920) / 3 = 2760 / 3 ≈ 920
This solution is correct!
Solution 3:
2003, 537, 220
Verification:
(2003 + 537 + 220) / 3 = 2760 / 3 ≈ 920
This solution is correct!
Solution 4:
784, 12, 1964
Verification:
(784 + 12 + 1964) / 3 = 2760 / 3 ≈ 920
This solution is correct!
Solution 5:
666, 1523, 571
Verification:
(666 + 1523 + 571) / 3 = 2760 / 3 ≈ 920
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 2760 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.