What three numbers have an average of 120?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 120. This means if we add these three numbers together and divide by 3, we should get 120.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 120 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 120 * 3 = x + y + z
- So, the sum of our three numbers should be: 360
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 360.
Solution 1:
120, 120, 120
Verification:
(120 + 120 + 120) / 3 = 360 / 3 ≈ 120
This solution is correct!
Solution 2:
120, 120, 120
Verification:
(120 + 120 + 120) / 3 = 360 / 3 ≈ 120
This solution is correct!
Solution 3:
227, 52, 81
Verification:
(227 + 52 + 81) / 3 = 360 / 3 ≈ 120
This solution is correct!
Solution 4:
83, 226, 51
Verification:
(83 + 226 + 51) / 3 = 360 / 3 ≈ 120
This solution is correct!
Solution 5:
316, 17, 27
Verification:
(316 + 17 + 27) / 3 = 360 / 3 ≈ 120
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 360 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.