What three numbers have an average of 617?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 617. This means if we add these three numbers together and divide by 3, we should get 617.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 617 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 617 * 3 = x + y + z
- So, the sum of our three numbers should be: 1851
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1851.
Solution 1:
617, 617, 617
Verification:
(617 + 617 + 617) / 3 = 1851 / 3 ≈ 617
This solution is correct!
Solution 2:
617, 617, 617
Verification:
(617 + 617 + 617) / 3 = 1851 / 3 ≈ 617
This solution is correct!
Solution 3:
390, 198, 1263
Verification:
(390 + 198 + 1263) / 3 = 1851 / 3 ≈ 617
This solution is correct!
Solution 4:
1743, 18, 90
Verification:
(1743 + 18 + 90) / 3 = 1851 / 3 ≈ 617
This solution is correct!
Solution 5:
1838, 4, 9
Verification:
(1838 + 4 + 9) / 3 = 1851 / 3 ≈ 617
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 1851 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.