What three numbers have an average of 54?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 54. This means if we add these three numbers together and divide by 3, we should get 54.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 54 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 54 * 3 = x + y + z
- So, the sum of our three numbers should be: 162
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 162.
Solution 1:
54, 54, 54
Verification:
(54 + 54 + 54) / 3 = 162 / 3 ≈ 54
This solution is correct!
Solution 2:
54, 54, 54
Verification:
(54 + 54 + 54) / 3 = 162 / 3 ≈ 54
This solution is correct!
Solution 3:
50, 70, 42
Verification:
(50 + 70 + 42) / 3 = 162 / 3 ≈ 54
This solution is correct!
Solution 4:
116, 32, 14
Verification:
(116 + 32 + 14) / 3 = 162 / 3 ≈ 54
This solution is correct!
Solution 5:
60, 68, 34
Verification:
(60 + 68 + 34) / 3 = 162 / 3 ≈ 54
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 162 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.