What three numbers have an average of 73?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 73. This means if we add these three numbers together and divide by 3, we should get 73.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 73 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 73 * 3 = x + y + z
- So, the sum of our three numbers should be: 219
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 219.
Solution 1:
73, 73, 73
Verification:
(73 + 73 + 73) / 3 = 219 / 3 ≈ 73
This solution is correct!
Solution 2:
73, 73, 73
Verification:
(73 + 73 + 73) / 3 = 219 / 3 ≈ 73
This solution is correct!
Solution 3:
3, 126, 90
Verification:
(3 + 126 + 90) / 3 = 219 / 3 ≈ 73
This solution is correct!
Solution 4:
194, 17, 8
Verification:
(194 + 17 + 8) / 3 = 219 / 3 ≈ 73
This solution is correct!
Solution 5:
151, 19, 49
Verification:
(151 + 19 + 49) / 3 = 219 / 3 ≈ 73
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 219 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.