What three numbers have an average of 82?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 82. This means if we add these three numbers together and divide by 3, we should get 82.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 82 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 82 * 3 = x + y + z
- So, the sum of our three numbers should be: 246
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 246.
Solution 1:
82, 82, 82
Verification:
(82 + 82 + 82) / 3 = 246 / 3 ≈ 82
This solution is correct!
Solution 2:
82, 82, 82
Verification:
(82 + 82 + 82) / 3 = 246 / 3 ≈ 82
This solution is correct!
Solution 3:
5, 185, 56
Verification:
(5 + 185 + 56) / 3 = 246 / 3 ≈ 82
This solution is correct!
Solution 4:
58, 171, 17
Verification:
(58 + 171 + 17) / 3 = 246 / 3 ≈ 82
This solution is correct!
Solution 5:
73, 76, 97
Verification:
(73 + 76 + 97) / 3 = 246 / 3 ≈ 82
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 246 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.