What three numbers have an average of 637?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 637. This means if we add these three numbers together and divide by 3, we should get 637.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 637 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 637 * 3 = x + y + z
- So, the sum of our three numbers should be: 1911
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1911.
Solution 1:
637, 637, 637
Verification:
(637 + 637 + 637) / 3 = 1911 / 3 ≈ 637
This solution is correct!
Solution 2:
637, 637, 637
Verification:
(637 + 637 + 637) / 3 = 1911 / 3 ≈ 637
This solution is correct!
Solution 3:
1420, 475, 16
Verification:
(1420 + 475 + 16) / 3 = 1911 / 3 ≈ 637
This solution is correct!
Solution 4:
1613, 71, 227
Verification:
(1613 + 71 + 227) / 3 = 1911 / 3 ≈ 637
This solution is correct!
Solution 5:
1135, 284, 492
Verification:
(1135 + 284 + 492) / 3 = 1911 / 3 ≈ 637
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 1911 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.