What three numbers have an average of 51?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 51. This means if we add these three numbers together and divide by 3, we should get 51.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 51 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 51 * 3 = x + y + z
- So, the sum of our three numbers should be: 153
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 153.
Solution 1:
51, 51, 51
Verification:
(51 + 51 + 51) / 3 = 153 / 3 ≈ 51
This solution is correct!
Solution 2:
51, 51, 51
Verification:
(51 + 51 + 51) / 3 = 153 / 3 ≈ 51
This solution is correct!
Solution 3:
37, 16, 100
Verification:
(37 + 16 + 100) / 3 = 153 / 3 ≈ 51
This solution is correct!
Solution 4:
125, 1, 27
Verification:
(125 + 1 + 27) / 3 = 153 / 3 ≈ 51
This solution is correct!
Solution 5:
27, 115, 11
Verification:
(27 + 115 + 11) / 3 = 153 / 3 ≈ 51
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 153 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.