What three numbers have an average of 72?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 72. This means if we add these three numbers together and divide by 3, we should get 72.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 72 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 72 * 3 = x + y + z
- So, the sum of our three numbers should be: 216
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 216.
Solution 1:
72, 72, 72
Verification:
(72 + 72 + 72) / 3 = 216 / 3 ≈ 72
This solution is correct!
Solution 2:
72, 72, 72
Verification:
(72 + 72 + 72) / 3 = 216 / 3 ≈ 72
This solution is correct!
Solution 3:
3, 15, 198
Verification:
(3 + 15 + 198) / 3 = 216 / 3 ≈ 72
This solution is correct!
Solution 4:
89, 85, 42
Verification:
(89 + 85 + 42) / 3 = 216 / 3 ≈ 72
This solution is correct!
Solution 5:
44, 40, 132
Verification:
(44 + 40 + 132) / 3 = 216 / 3 ≈ 72
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 216 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.