What three numbers have an average of 442?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 442. This means if we add these three numbers together and divide by 3, we should get 442.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 442 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 442 * 3 = x + y + z
- So, the sum of our three numbers should be: 1326
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1326.
Solution 1:
442, 442, 442
Verification:
(442 + 442 + 442) / 3 = 1326 / 3 ≈ 442
This solution is correct!
Solution 2:
442, 442, 442
Verification:
(442 + 442 + 442) / 3 = 1326 / 3 ≈ 442
This solution is correct!
Solution 3:
988, 67, 271
Verification:
(988 + 67 + 271) / 3 = 1326 / 3 ≈ 442
This solution is correct!
Solution 4:
998, 263, 65
Verification:
(998 + 263 + 65) / 3 = 1326 / 3 ≈ 442
This solution is correct!
Solution 5:
333, 671, 322
Verification:
(333 + 671 + 322) / 3 = 1326 / 3 ≈ 442
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 1326 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.