What three numbers have an average of 422?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 422. This means if we add these three numbers together and divide by 3, we should get 422.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 422 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 422 * 3 = x + y + z
- So, the sum of our three numbers should be: 1266
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1266.
Solution 1:
422, 422, 422
Verification:
(422 + 422 + 422) / 3 = 1266 / 3 ≈ 422
This solution is correct!
Solution 2:
422, 422, 422
Verification:
(422 + 422 + 422) / 3 = 1266 / 3 ≈ 422
This solution is correct!
Solution 3:
928, 42, 296
Verification:
(928 + 42 + 296) / 3 = 1266 / 3 ≈ 422
This solution is correct!
Solution 4:
678, 504, 84
Verification:
(678 + 504 + 84) / 3 = 1266 / 3 ≈ 422
This solution is correct!
Solution 5:
160, 187, 919
Verification:
(160 + 187 + 919) / 3 = 1266 / 3 ≈ 422
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 1266 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.