What three numbers have an average of 55?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 55. This means if we add these three numbers together and divide by 3, we should get 55.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 55 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 55 * 3 = x + y + z
- So, the sum of our three numbers should be: 165
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 165.
Solution 1:
55, 55, 55
Verification:
(55 + 55 + 55) / 3 = 165 / 3 ≈ 55
This solution is correct!
Solution 2:
55, 55, 55
Verification:
(55 + 55 + 55) / 3 = 165 / 3 ≈ 55
This solution is correct!
Solution 3:
63, 58, 44
Verification:
(63 + 58 + 44) / 3 = 165 / 3 ≈ 55
This solution is correct!
Solution 4:
160, 4, 1
Verification:
(160 + 4 + 1) / 3 = 165 / 3 ≈ 55
This solution is correct!
Solution 5:
142, 8, 15
Verification:
(142 + 8 + 15) / 3 = 165 / 3 ≈ 55
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 165 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.