What three numbers have an average of 549?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 549. This means if we add these three numbers together and divide by 3, we should get 549.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 549 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 549 * 3 = x + y + z
- So, the sum of our three numbers should be: 1647
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1647.
Solution 1:
549, 549, 549
Verification:
(549 + 549 + 549) / 3 = 1647 / 3 ≈ 549
This solution is correct!
Solution 2:
549, 549, 549
Verification:
(549 + 549 + 549) / 3 = 1647 / 3 ≈ 549
This solution is correct!
Solution 3:
253, 99, 1295
Verification:
(253 + 99 + 1295) / 3 = 1647 / 3 ≈ 549
This solution is correct!
Solution 4:
402, 301, 944
Verification:
(402 + 301 + 944) / 3 = 1647 / 3 ≈ 549
This solution is correct!
Solution 5:
980, 80, 587
Verification:
(980 + 80 + 587) / 3 = 1647 / 3 ≈ 549
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 1647 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.