What three numbers have an average of 371?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 371. This means if we add these three numbers together and divide by 3, we should get 371.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 371 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 371 * 3 = x + y + z
- So, the sum of our three numbers should be: 1113
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1113.
Solution 1:
371, 371, 371
Verification:
(371 + 371 + 371) / 3 = 1113 / 3 ≈ 371
This solution is correct!
Solution 2:
371, 371, 371
Verification:
(371 + 371 + 371) / 3 = 1113 / 3 ≈ 371
This solution is correct!
Solution 3:
458, 265, 390
Verification:
(458 + 265 + 390) / 3 = 1113 / 3 ≈ 371
This solution is correct!
Solution 4:
485, 118, 510
Verification:
(485 + 118 + 510) / 3 = 1113 / 3 ≈ 371
This solution is correct!
Solution 5:
233, 251, 629
Verification:
(233 + 251 + 629) / 3 = 1113 / 3 ≈ 371
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 1113 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.