What three numbers have an average of 60?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 60. This means if we add these three numbers together and divide by 3, we should get 60.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 60 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 60 * 3 = x + y + z
- So, the sum of our three numbers should be: 180
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 180.
Solution 1:
60, 60, 60
Verification:
(60 + 60 + 60) / 3 = 180 / 3 ≈ 60
This solution is correct!
Solution 2:
60, 60, 60
Verification:
(60 + 60 + 60) / 3 = 180 / 3 ≈ 60
This solution is correct!
Solution 3:
176, 2, 2
Verification:
(176 + 2 + 2) / 3 = 180 / 3 ≈ 60
This solution is correct!
Solution 4:
144, 25, 11
Verification:
(144 + 25 + 11) / 3 = 180 / 3 ≈ 60
This solution is correct!
Solution 5:
76, 85, 19
Verification:
(76 + 85 + 19) / 3 = 180 / 3 ≈ 60
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 180 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.