What three numbers have an average of 324?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 324. This means if we add these three numbers together and divide by 3, we should get 324.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 324 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 324 * 3 = x + y + z
- So, the sum of our three numbers should be: 972
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 972.
Solution 1:
324, 324, 324
Verification:
(324 + 324 + 324) / 3 = 972 / 3 ≈ 324
This solution is correct!
Solution 2:
324, 324, 324
Verification:
(324 + 324 + 324) / 3 = 972 / 3 ≈ 324
This solution is correct!
Solution 3:
38, 346, 588
Verification:
(38 + 346 + 588) / 3 = 972 / 3 ≈ 324
This solution is correct!
Solution 4:
276, 307, 389
Verification:
(276 + 307 + 389) / 3 = 972 / 3 ≈ 324
This solution is correct!
Solution 5:
104, 560, 308
Verification:
(104 + 560 + 308) / 3 = 972 / 3 ≈ 324
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 972 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.