What three numbers have an average of 860?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 860. This means if we add these three numbers together and divide by 3, we should get 860.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 860 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 860 * 3 = x + y + z
- So, the sum of our three numbers should be: 2580
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2580.
Solution 1:
860, 860, 860
Verification:
(860 + 860 + 860) / 3 = 2580 / 3 ≈ 860
This solution is correct!
Solution 2:
860, 860, 860
Verification:
(860 + 860 + 860) / 3 = 2580 / 3 ≈ 860
This solution is correct!
Solution 3:
402, 11, 2167
Verification:
(402 + 11 + 2167) / 3 = 2580 / 3 ≈ 860
This solution is correct!
Solution 4:
1800, 200, 580
Verification:
(1800 + 200 + 580) / 3 = 2580 / 3 ≈ 860
This solution is correct!
Solution 5:
650, 1772, 158
Verification:
(650 + 1772 + 158) / 3 = 2580 / 3 ≈ 860
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 2580 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.