What three numbers have an average of 58?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 58. This means if we add these three numbers together and divide by 3, we should get 58.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 58 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 58 * 3 = x + y + z
- So, the sum of our three numbers should be: 174
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 174.
Solution 1:
58, 58, 58
Verification:
(58 + 58 + 58) / 3 = 174 / 3 ≈ 58
This solution is correct!
Solution 2:
58, 58, 58
Verification:
(58 + 58 + 58) / 3 = 174 / 3 ≈ 58
This solution is correct!
Solution 3:
114, 28, 32
Verification:
(114 + 28 + 32) / 3 = 174 / 3 ≈ 58
This solution is correct!
Solution 4:
112, 13, 49
Verification:
(112 + 13 + 49) / 3 = 174 / 3 ≈ 58
This solution is correct!
Solution 5:
164, 5, 5
Verification:
(164 + 5 + 5) / 3 = 174 / 3 ≈ 58
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 174 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.