What three numbers have an average of 389?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 389. This means if we add these three numbers together and divide by 3, we should get 389.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 389 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 389 * 3 = x + y + z
- So, the sum of our three numbers should be: 1167
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1167.
Solution 1:
389, 389, 389
Verification:
(389 + 389 + 389) / 3 = 1167 / 3 ≈ 389
This solution is correct!
Solution 2:
389, 389, 389
Verification:
(389 + 389 + 389) / 3 = 1167 / 3 ≈ 389
This solution is correct!
Solution 3:
243, 286, 638
Verification:
(243 + 286 + 638) / 3 = 1167 / 3 ≈ 389
This solution is correct!
Solution 4:
857, 83, 227
Verification:
(857 + 83 + 227) / 3 = 1167 / 3 ≈ 389
This solution is correct!
Solution 5:
794, 13, 360
Verification:
(794 + 13 + 360) / 3 = 1167 / 3 ≈ 389
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 1167 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.