What three numbers have an average of 851?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 851. This means if we add these three numbers together and divide by 3, we should get 851.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 851 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 851 * 3 = x + y + z
- So, the sum of our three numbers should be: 2553
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2553.
Solution 1:
851, 851, 851
Verification:
(851 + 851 + 851) / 3 = 2553 / 3 ≈ 851
This solution is correct!
Solution 2:
851, 851, 851
Verification:
(851 + 851 + 851) / 3 = 2553 / 3 ≈ 851
This solution is correct!
Solution 3:
28, 960, 1565
Verification:
(28 + 960 + 1565) / 3 = 2553 / 3 ≈ 851
This solution is correct!
Solution 4:
1344, 194, 1015
Verification:
(1344 + 194 + 1015) / 3 = 2553 / 3 ≈ 851
This solution is correct!
Solution 5:
1865, 386, 302
Verification:
(1865 + 386 + 302) / 3 = 2553 / 3 ≈ 851
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 2553 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.