What three numbers have an average of 237?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 237. This means if we add these three numbers together and divide by 3, we should get 237.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 237 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 237 * 3 = x + y + z
- So, the sum of our three numbers should be: 711
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 711.
Solution 1:
237, 237, 237
Verification:
(237 + 237 + 237) / 3 = 711 / 3 ≈ 237
This solution is correct!
Solution 2:
237, 237, 237
Verification:
(237 + 237 + 237) / 3 = 711 / 3 ≈ 237
This solution is correct!
Solution 3:
271, 147, 293
Verification:
(271 + 147 + 293) / 3 = 711 / 3 ≈ 237
This solution is correct!
Solution 4:
111, 85, 515
Verification:
(111 + 85 + 515) / 3 = 711 / 3 ≈ 237
This solution is correct!
Solution 5:
370, 321, 20
Verification:
(370 + 321 + 20) / 3 = 711 / 3 ≈ 237
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 711 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.