What three numbers have an average of 186?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 186. This means if we add these three numbers together and divide by 3, we should get 186.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 186 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 186 * 3 = x + y + z
- So, the sum of our three numbers should be: 558
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 558.
Solution 1:
186, 186, 186
Verification:
(186 + 186 + 186) / 3 = 558 / 3 ≈ 186
This solution is correct!
Solution 2:
186, 186, 186
Verification:
(186 + 186 + 186) / 3 = 558 / 3 ≈ 186
This solution is correct!
Solution 3:
462, 77, 19
Verification:
(462 + 77 + 19) / 3 = 558 / 3 ≈ 186
This solution is correct!
Solution 4:
429, 25, 104
Verification:
(429 + 25 + 104) / 3 = 558 / 3 ≈ 186
This solution is correct!
Solution 5:
393, 93, 72
Verification:
(393 + 93 + 72) / 3 = 558 / 3 ≈ 186
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 558 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.