What three numbers have an average of 858?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 858. This means if we add these three numbers together and divide by 3, we should get 858.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 858 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 858 * 3 = x + y + z
- So, the sum of our three numbers should be: 2574
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2574.
Solution 1:
858, 858, 858
Verification:
(858 + 858 + 858) / 3 = 2574 / 3 ≈ 858
This solution is correct!
Solution 2:
858, 858, 858
Verification:
(858 + 858 + 858) / 3 = 2574 / 3 ≈ 858
This solution is correct!
Solution 3:
832, 880, 862
Verification:
(832 + 880 + 862) / 3 = 2574 / 3 ≈ 858
This solution is correct!
Solution 4:
987, 477, 1110
Verification:
(987 + 477 + 1110) / 3 = 2574 / 3 ≈ 858
This solution is correct!
Solution 5:
1759, 105, 710
Verification:
(1759 + 105 + 710) / 3 = 2574 / 3 ≈ 858
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 2574 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.