What three numbers have an average of 119?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 119. This means if we add these three numbers together and divide by 3, we should get 119.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 119 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 119 * 3 = x + y + z
- So, the sum of our three numbers should be: 357
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 357.
Solution 1:
119, 119, 119
Verification:
(119 + 119 + 119) / 3 = 357 / 3 ≈ 119
This solution is correct!
Solution 2:
119, 119, 119
Verification:
(119 + 119 + 119) / 3 = 357 / 3 ≈ 119
This solution is correct!
Solution 3:
56, 184, 117
Verification:
(56 + 184 + 117) / 3 = 357 / 3 ≈ 119
This solution is correct!
Solution 4:
235, 121, 1
Verification:
(235 + 121 + 1) / 3 = 357 / 3 ≈ 119
This solution is correct!
Solution 5:
102, 243, 12
Verification:
(102 + 243 + 12) / 3 = 357 / 3 ≈ 119
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 357 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.