What three numbers have an average of 37?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 37. This means if we add these three numbers together and divide by 3, we should get 37.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 37 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 37 * 3 = x + y + z
- So, the sum of our three numbers should be: 111
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 111.
Solution 1:
37, 37, 37
Verification:
(37 + 37 + 37) / 3 = 111 / 3 ≈ 37
This solution is correct!
Solution 2:
37, 37, 37
Verification:
(37 + 37 + 37) / 3 = 111 / 3 ≈ 37
This solution is correct!
Solution 3:
96, 6, 9
Verification:
(96 + 6 + 9) / 3 = 111 / 3 ≈ 37
This solution is correct!
Solution 4:
81, 7, 23
Verification:
(81 + 7 + 23) / 3 = 111 / 3 ≈ 37
This solution is correct!
Solution 5:
99, 7, 5
Verification:
(99 + 7 + 5) / 3 = 111 / 3 ≈ 37
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 111 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.