What three numbers have an average of 686?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 686. This means if we add these three numbers together and divide by 3, we should get 686.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 686 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 686 * 3 = x + y + z
- So, the sum of our three numbers should be: 2058
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2058.
Solution 1:
686, 686, 686
Verification:
(686 + 686 + 686) / 3 = 2058 / 3 ≈ 686
This solution is correct!
Solution 2:
686, 686, 686
Verification:
(686 + 686 + 686) / 3 = 2058 / 3 ≈ 686
This solution is correct!
Solution 3:
881, 154, 1023
Verification:
(881 + 154 + 1023) / 3 = 2058 / 3 ≈ 686
This solution is correct!
Solution 4:
1749, 215, 94
Verification:
(1749 + 215 + 94) / 3 = 2058 / 3 ≈ 686
This solution is correct!
Solution 5:
1215, 462, 381
Verification:
(1215 + 462 + 381) / 3 = 2058 / 3 ≈ 686
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 2058 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.