What three numbers have an average of 322?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 322. This means if we add these three numbers together and divide by 3, we should get 322.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 322 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 322 * 3 = x + y + z
- So, the sum of our three numbers should be: 966
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 966.
Solution 1:
322, 322, 322
Verification:
(322 + 322 + 322) / 3 = 966 / 3 ≈ 322
This solution is correct!
Solution 2:
322, 322, 322
Verification:
(322 + 322 + 322) / 3 = 966 / 3 ≈ 322
This solution is correct!
Solution 3:
860, 99, 7
Verification:
(860 + 99 + 7) / 3 = 966 / 3 ≈ 322
This solution is correct!
Solution 4:
575, 174, 217
Verification:
(575 + 174 + 217) / 3 = 966 / 3 ≈ 322
This solution is correct!
Solution 5:
288, 157, 521
Verification:
(288 + 157 + 521) / 3 = 966 / 3 ≈ 322
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 966 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.