What three numbers have an average of 57?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 57. This means if we add these three numbers together and divide by 3, we should get 57.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 57 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 57 * 3 = x + y + z
- So, the sum of our three numbers should be: 171
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 171.
Solution 1:
57, 57, 57
Verification:
(57 + 57 + 57) / 3 = 171 / 3 ≈ 57
This solution is correct!
Solution 2:
57, 57, 57
Verification:
(57 + 57 + 57) / 3 = 171 / 3 ≈ 57
This solution is correct!
Solution 3:
48, 43, 80
Verification:
(48 + 43 + 80) / 3 = 171 / 3 ≈ 57
This solution is correct!
Solution 4:
141, 21, 9
Verification:
(141 + 21 + 9) / 3 = 171 / 3 ≈ 57
This solution is correct!
Solution 5:
113, 1, 57
Verification:
(113 + 1 + 57) / 3 = 171 / 3 ≈ 57
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 171 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.