What three numbers have an average of 536?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 536. This means if we add these three numbers together and divide by 3, we should get 536.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 536 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 536 * 3 = x + y + z
- So, the sum of our three numbers should be: 1608
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1608.
Solution 1:
536, 536, 536
Verification:
(536 + 536 + 536) / 3 = 1608 / 3 ≈ 536
This solution is correct!
Solution 2:
536, 536, 536
Verification:
(536 + 536 + 536) / 3 = 1608 / 3 ≈ 536
This solution is correct!
Solution 3:
1396, 14, 198
Verification:
(1396 + 14 + 198) / 3 = 1608 / 3 ≈ 536
This solution is correct!
Solution 4:
288, 600, 720
Verification:
(288 + 600 + 720) / 3 = 1608 / 3 ≈ 536
This solution is correct!
Solution 5:
1463, 21, 124
Verification:
(1463 + 21 + 124) / 3 = 1608 / 3 ≈ 536
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 1608 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.