What three numbers have an average of 899?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 899. This means if we add these three numbers together and divide by 3, we should get 899.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 899 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 899 * 3 = x + y + z
- So, the sum of our three numbers should be: 2697
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2697.
Solution 1:
899, 899, 899
Verification:
(899 + 899 + 899) / 3 = 2697 / 3 ≈ 899
This solution is correct!
Solution 2:
899, 899, 899
Verification:
(899 + 899 + 899) / 3 = 2697 / 3 ≈ 899
This solution is correct!
Solution 3:
1493, 830, 374
Verification:
(1493 + 830 + 374) / 3 = 2697 / 3 ≈ 899
This solution is correct!
Solution 4:
1096, 832, 769
Verification:
(1096 + 832 + 769) / 3 = 2697 / 3 ≈ 899
This solution is correct!
Solution 5:
1071, 957, 669
Verification:
(1071 + 957 + 669) / 3 = 2697 / 3 ≈ 899
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 2697 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.