What three numbers have an average of 862?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 862. This means if we add these three numbers together and divide by 3, we should get 862.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 862 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 862 * 3 = x + y + z
- So, the sum of our three numbers should be: 2586
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2586.
Solution 1:
862, 862, 862
Verification:
(862 + 862 + 862) / 3 = 2586 / 3 ≈ 862
This solution is correct!
Solution 2:
862, 862, 862
Verification:
(862 + 862 + 862) / 3 = 2586 / 3 ≈ 862
This solution is correct!
Solution 3:
1121, 1231, 234
Verification:
(1121 + 1231 + 234) / 3 = 2586 / 3 ≈ 862
This solution is correct!
Solution 4:
6, 1189, 1391
Verification:
(6 + 1189 + 1391) / 3 = 2586 / 3 ≈ 862
This solution is correct!
Solution 5:
84, 2206, 296
Verification:
(84 + 2206 + 296) / 3 = 2586 / 3 ≈ 862
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 2586 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.