What three numbers have an average of 671?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 671. This means if we add these three numbers together and divide by 3, we should get 671.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 671 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 671 * 3 = x + y + z
- So, the sum of our three numbers should be: 2013
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2013.
Solution 1:
671, 671, 671
Verification:
(671 + 671 + 671) / 3 = 2013 / 3 ≈ 671
This solution is correct!
Solution 2:
671, 671, 671
Verification:
(671 + 671 + 671) / 3 = 2013 / 3 ≈ 671
This solution is correct!
Solution 3:
1958, 33, 22
Verification:
(1958 + 33 + 22) / 3 = 2013 / 3 ≈ 671
This solution is correct!
Solution 4:
1298, 59, 656
Verification:
(1298 + 59 + 656) / 3 = 2013 / 3 ≈ 671
This solution is correct!
Solution 5:
436, 1153, 424
Verification:
(436 + 1153 + 424) / 3 = 2013 / 3 ≈ 671
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 2013 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.