What three numbers have an average of 730?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 730. This means if we add these three numbers together and divide by 3, we should get 730.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 730 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 730 * 3 = x + y + z
- So, the sum of our three numbers should be: 2190
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2190.
Solution 1:
730, 730, 730
Verification:
(730 + 730 + 730) / 3 = 2190 / 3 ≈ 730
This solution is correct!
Solution 2:
730, 730, 730
Verification:
(730 + 730 + 730) / 3 = 2190 / 3 ≈ 730
This solution is correct!
Solution 3:
1455, 122, 613
Verification:
(1455 + 122 + 613) / 3 = 2190 / 3 ≈ 730
This solution is correct!
Solution 4:
2104, 69, 17
Verification:
(2104 + 69 + 17) / 3 = 2190 / 3 ≈ 730
This solution is correct!
Solution 5:
1619, 4, 567
Verification:
(1619 + 4 + 567) / 3 = 2190 / 3 ≈ 730
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 2190 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.