What three numbers have an average of 31?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 31. This means if we add these three numbers together and divide by 3, we should get 31.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 31 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 31 * 3 = x + y + z
- So, the sum of our three numbers should be: 93
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 93.
Solution 1:
31, 31, 31
Verification:
(31 + 31 + 31) / 3 = 93 / 3 ≈ 31
This solution is correct!
Solution 2:
31, 31, 31
Verification:
(31 + 31 + 31) / 3 = 93 / 3 ≈ 31
This solution is correct!
Solution 3:
64, 28, 1
Verification:
(64 + 28 + 1) / 3 = 93 / 3 ≈ 31
This solution is correct!
Solution 4:
28, 32, 33
Verification:
(28 + 32 + 33) / 3 = 93 / 3 ≈ 31
This solution is correct!
Solution 5:
11, 59, 23
Verification:
(11 + 59 + 23) / 3 = 93 / 3 ≈ 31
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 93 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.