What three numbers have an average of 853?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 853. This means if we add these three numbers together and divide by 3, we should get 853.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 853 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 853 * 3 = x + y + z
- So, the sum of our three numbers should be: 2559
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2559.
Solution 1:
853, 853, 853
Verification:
(853 + 853 + 853) / 3 = 2559 / 3 ≈ 853
This solution is correct!
Solution 2:
853, 853, 853
Verification:
(853 + 853 + 853) / 3 = 2559 / 3 ≈ 853
This solution is correct!
Solution 3:
1976, 461, 122
Verification:
(1976 + 461 + 122) / 3 = 2559 / 3 ≈ 853
This solution is correct!
Solution 4:
1971, 514, 74
Verification:
(1971 + 514 + 74) / 3 = 2559 / 3 ≈ 853
This solution is correct!
Solution 5:
312, 57, 2190
Verification:
(312 + 57 + 2190) / 3 = 2559 / 3 ≈ 853
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 2559 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.