What three numbers have an average of 52?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 52. This means if we add these three numbers together and divide by 3, we should get 52.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 52 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 52 * 3 = x + y + z
- So, the sum of our three numbers should be: 156
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 156.
Solution 1:
52, 52, 52
Verification:
(52 + 52 + 52) / 3 = 156 / 3 ≈ 52
This solution is correct!
Solution 2:
52, 52, 52
Verification:
(52 + 52 + 52) / 3 = 156 / 3 ≈ 52
This solution is correct!
Solution 3:
109, 19, 28
Verification:
(109 + 19 + 28) / 3 = 156 / 3 ≈ 52
This solution is correct!
Solution 4:
100, 22, 34
Verification:
(100 + 22 + 34) / 3 = 156 / 3 ≈ 52
This solution is correct!
Solution 5:
62, 92, 2
Verification:
(62 + 92 + 2) / 3 = 156 / 3 ≈ 52
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 156 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.