What three numbers have an average of 83?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 83. This means if we add these three numbers together and divide by 3, we should get 83.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 83 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 83 * 3 = x + y + z
- So, the sum of our three numbers should be: 249
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 249.
Solution 1:
83, 83, 83
Verification:
(83 + 83 + 83) / 3 = 249 / 3 ≈ 83
This solution is correct!
Solution 2:
83, 83, 83
Verification:
(83 + 83 + 83) / 3 = 249 / 3 ≈ 83
This solution is correct!
Solution 3:
150, 46, 53
Verification:
(150 + 46 + 53) / 3 = 249 / 3 ≈ 83
This solution is correct!
Solution 4:
223, 15, 11
Verification:
(223 + 15 + 11) / 3 = 249 / 3 ≈ 83
This solution is correct!
Solution 5:
166, 60, 23
Verification:
(166 + 60 + 23) / 3 = 249 / 3 ≈ 83
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 249 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.