What three numbers have an average of 619?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 619. This means if we add these three numbers together and divide by 3, we should get 619.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 619 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 619 * 3 = x + y + z
- So, the sum of our three numbers should be: 1857
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1857.
Solution 1:
619, 619, 619
Verification:
(619 + 619 + 619) / 3 = 1857 / 3 ≈ 619
This solution is correct!
Solution 2:
619, 619, 619
Verification:
(619 + 619 + 619) / 3 = 1857 / 3 ≈ 619
This solution is correct!
Solution 3:
1712, 65, 80
Verification:
(1712 + 65 + 80) / 3 = 1857 / 3 ≈ 619
This solution is correct!
Solution 4:
204, 1136, 517
Verification:
(204 + 1136 + 517) / 3 = 1857 / 3 ≈ 619
This solution is correct!
Solution 5:
393, 375, 1089
Verification:
(393 + 375 + 1089) / 3 = 1857 / 3 ≈ 619
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 1857 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.