What three numbers have an average of 599?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 599. This means if we add these three numbers together and divide by 3, we should get 599.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 599 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 599 * 3 = x + y + z
- So, the sum of our three numbers should be: 1797
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1797.
Solution 1:
599, 599, 599
Verification:
(599 + 599 + 599) / 3 = 1797 / 3 ≈ 599
This solution is correct!
Solution 2:
599, 599, 599
Verification:
(599 + 599 + 599) / 3 = 1797 / 3 ≈ 599
This solution is correct!
Solution 3:
1391, 139, 267
Verification:
(1391 + 139 + 267) / 3 = 1797 / 3 ≈ 599
This solution is correct!
Solution 4:
449, 1027, 321
Verification:
(449 + 1027 + 321) / 3 = 1797 / 3 ≈ 599
This solution is correct!
Solution 5:
634, 862, 301
Verification:
(634 + 862 + 301) / 3 = 1797 / 3 ≈ 599
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 1797 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.