What three numbers have an average of 131?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 131. This means if we add these three numbers together and divide by 3, we should get 131.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 131 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 131 * 3 = x + y + z
- So, the sum of our three numbers should be: 393
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 393.
Solution 1:
131, 131, 131
Verification:
(131 + 131 + 131) / 3 = 393 / 3 ≈ 131
This solution is correct!
Solution 2:
131, 131, 131
Verification:
(131 + 131 + 131) / 3 = 393 / 3 ≈ 131
This solution is correct!
Solution 3:
238, 65, 90
Verification:
(238 + 65 + 90) / 3 = 393 / 3 ≈ 131
This solution is correct!
Solution 4:
10, 299, 84
Verification:
(10 + 299 + 84) / 3 = 393 / 3 ≈ 131
This solution is correct!
Solution 5:
212, 4, 177
Verification:
(212 + 4 + 177) / 3 = 393 / 3 ≈ 131
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 393 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.