What three numbers have an average of 337?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 337. This means if we add these three numbers together and divide by 3, we should get 337.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 337 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 337 * 3 = x + y + z
- So, the sum of our three numbers should be: 1011
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1011.
Solution 1:
337, 337, 337
Verification:
(337 + 337 + 337) / 3 = 1011 / 3 ≈ 337
This solution is correct!
Solution 2:
337, 337, 337
Verification:
(337 + 337 + 337) / 3 = 1011 / 3 ≈ 337
This solution is correct!
Solution 3:
844, 20, 147
Verification:
(844 + 20 + 147) / 3 = 1011 / 3 ≈ 337
This solution is correct!
Solution 4:
977, 26, 8
Verification:
(977 + 26 + 8) / 3 = 1011 / 3 ≈ 337
This solution is correct!
Solution 5:
164, 736, 111
Verification:
(164 + 736 + 111) / 3 = 1011 / 3 ≈ 337
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 1011 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.