What three numbers have an average of 92?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 92. This means if we add these three numbers together and divide by 3, we should get 92.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 92 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 92 * 3 = x + y + z
- So, the sum of our three numbers should be: 276
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 276.
Solution 1:
92, 92, 92
Verification:
(92 + 92 + 92) / 3 = 276 / 3 ≈ 92
This solution is correct!
Solution 2:
92, 92, 92
Verification:
(92 + 92 + 92) / 3 = 276 / 3 ≈ 92
This solution is correct!
Solution 3:
107, 110, 59
Verification:
(107 + 110 + 59) / 3 = 276 / 3 ≈ 92
This solution is correct!
Solution 4:
209, 44, 23
Verification:
(209 + 44 + 23) / 3 = 276 / 3 ≈ 92
This solution is correct!
Solution 5:
10, 107, 159
Verification:
(10 + 107 + 159) / 3 = 276 / 3 ≈ 92
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 276 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.