What three numbers have an average of 81?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 81. This means if we add these three numbers together and divide by 3, we should get 81.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 81 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 81 * 3 = x + y + z
- So, the sum of our three numbers should be: 243
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 243.
Solution 1:
81, 81, 81
Verification:
(81 + 81 + 81) / 3 = 243 / 3 ≈ 81
This solution is correct!
Solution 2:
81, 81, 81
Verification:
(81 + 81 + 81) / 3 = 243 / 3 ≈ 81
This solution is correct!
Solution 3:
118, 36, 89
Verification:
(118 + 36 + 89) / 3 = 243 / 3 ≈ 81
This solution is correct!
Solution 4:
69, 61, 113
Verification:
(69 + 61 + 113) / 3 = 243 / 3 ≈ 81
This solution is correct!
Solution 5:
50, 189, 4
Verification:
(50 + 189 + 4) / 3 = 243 / 3 ≈ 81
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 243 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.