What three numbers have an average of 137?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 137. This means if we add these three numbers together and divide by 3, we should get 137.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 137 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 137 * 3 = x + y + z
- So, the sum of our three numbers should be: 411
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 411.
Solution 1:
137, 137, 137
Verification:
(137 + 137 + 137) / 3 = 411 / 3 ≈ 137
This solution is correct!
Solution 2:
137, 137, 137
Verification:
(137 + 137 + 137) / 3 = 411 / 3 ≈ 137
This solution is correct!
Solution 3:
141, 252, 18
Verification:
(141 + 252 + 18) / 3 = 411 / 3 ≈ 137
This solution is correct!
Solution 4:
241, 78, 92
Verification:
(241 + 78 + 92) / 3 = 411 / 3 ≈ 137
This solution is correct!
Solution 5:
316, 78, 17
Verification:
(316 + 78 + 17) / 3 = 411 / 3 ≈ 137
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 411 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.