What three numbers have an average of 97?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 97. This means if we add these three numbers together and divide by 3, we should get 97.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 97 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 97 * 3 = x + y + z
- So, the sum of our three numbers should be: 291
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 291.
Solution 1:
97, 97, 97
Verification:
(97 + 97 + 97) / 3 = 291 / 3 ≈ 97
This solution is correct!
Solution 2:
97, 97, 97
Verification:
(97 + 97 + 97) / 3 = 291 / 3 ≈ 97
This solution is correct!
Solution 3:
79, 52, 160
Verification:
(79 + 52 + 160) / 3 = 291 / 3 ≈ 97
This solution is correct!
Solution 4:
60, 132, 99
Verification:
(60 + 132 + 99) / 3 = 291 / 3 ≈ 97
This solution is correct!
Solution 5:
94, 71, 126
Verification:
(94 + 71 + 126) / 3 = 291 / 3 ≈ 97
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 291 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.