What three numbers have an average of 538?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 538. This means if we add these three numbers together and divide by 3, we should get 538.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 538 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 538 * 3 = x + y + z
- So, the sum of our three numbers should be: 1614
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1614.
Solution 1:
538, 538, 538
Verification:
(538 + 538 + 538) / 3 = 1614 / 3 ≈ 538
This solution is correct!
Solution 2:
538, 538, 538
Verification:
(538 + 538 + 538) / 3 = 1614 / 3 ≈ 538
This solution is correct!
Solution 3:
1271, 316, 27
Verification:
(1271 + 316 + 27) / 3 = 1614 / 3 ≈ 538
This solution is correct!
Solution 4:
268, 628, 718
Verification:
(268 + 628 + 718) / 3 = 1614 / 3 ≈ 538
This solution is correct!
Solution 5:
1021, 384, 209
Verification:
(1021 + 384 + 209) / 3 = 1614 / 3 ≈ 538
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 1614 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.