What three numbers have an average of 893?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 893. This means if we add these three numbers together and divide by 3, we should get 893.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 893 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 893 * 3 = x + y + z
- So, the sum of our three numbers should be: 2679
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2679.
Solution 1:
893, 893, 893
Verification:
(893 + 893 + 893) / 3 = 2679 / 3 ≈ 893
This solution is correct!
Solution 2:
893, 893, 893
Verification:
(893 + 893 + 893) / 3 = 2679 / 3 ≈ 893
This solution is correct!
Solution 3:
980, 228, 1471
Verification:
(980 + 228 + 1471) / 3 = 2679 / 3 ≈ 893
This solution is correct!
Solution 4:
2006, 636, 37
Verification:
(2006 + 636 + 37) / 3 = 2679 / 3 ≈ 893
This solution is correct!
Solution 5:
822, 1599, 258
Verification:
(822 + 1599 + 258) / 3 = 2679 / 3 ≈ 893
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 2679 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.