What three numbers have an average of 113?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 113. This means if we add these three numbers together and divide by 3, we should get 113.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 113 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 113 * 3 = x + y + z
- So, the sum of our three numbers should be: 339
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 339.
Solution 1:
113, 113, 113
Verification:
(113 + 113 + 113) / 3 = 339 / 3 ≈ 113
This solution is correct!
Solution 2:
113, 113, 113
Verification:
(113 + 113 + 113) / 3 = 339 / 3 ≈ 113
This solution is correct!
Solution 3:
37, 89, 213
Verification:
(37 + 89 + 213) / 3 = 339 / 3 ≈ 113
This solution is correct!
Solution 4:
294, 23, 22
Verification:
(294 + 23 + 22) / 3 = 339 / 3 ≈ 113
This solution is correct!
Solution 5:
272, 11, 56
Verification:
(272 + 11 + 56) / 3 = 339 / 3 ≈ 113
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 339 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.