What three numbers have an average of 187?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 187. This means if we add these three numbers together and divide by 3, we should get 187.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 187 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 187 * 3 = x + y + z
- So, the sum of our three numbers should be: 561
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 561.
Solution 1:
187, 187, 187
Verification:
(187 + 187 + 187) / 3 = 561 / 3 ≈ 187
This solution is correct!
Solution 2:
187, 187, 187
Verification:
(187 + 187 + 187) / 3 = 561 / 3 ≈ 187
This solution is correct!
Solution 3:
322, 16, 223
Verification:
(322 + 16 + 223) / 3 = 561 / 3 ≈ 187
This solution is correct!
Solution 4:
182, 125, 254
Verification:
(182 + 125 + 254) / 3 = 561 / 3 ≈ 187
This solution is correct!
Solution 5:
526, 8, 27
Verification:
(526 + 8 + 27) / 3 = 561 / 3 ≈ 187
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 561 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.