What three numbers have an average of 261?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 261. This means if we add these three numbers together and divide by 3, we should get 261.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 261 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 261 * 3 = x + y + z
- So, the sum of our three numbers should be: 783
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 783.
Solution 1:
261, 261, 261
Verification:
(261 + 261 + 261) / 3 = 783 / 3 ≈ 261
This solution is correct!
Solution 2:
261, 261, 261
Verification:
(261 + 261 + 261) / 3 = 783 / 3 ≈ 261
This solution is correct!
Solution 3:
694, 70, 19
Verification:
(694 + 70 + 19) / 3 = 783 / 3 ≈ 261
This solution is correct!
Solution 4:
447, 191, 145
Verification:
(447 + 191 + 145) / 3 = 783 / 3 ≈ 261
This solution is correct!
Solution 5:
395, 277, 111
Verification:
(395 + 277 + 111) / 3 = 783 / 3 ≈ 261
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 783 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.