What three numbers have an average of 413?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 413. This means if we add these three numbers together and divide by 3, we should get 413.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 413 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 413 * 3 = x + y + z
- So, the sum of our three numbers should be: 1239
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1239.
Solution 1:
413, 413, 413
Verification:
(413 + 413 + 413) / 3 = 1239 / 3 ≈ 413
This solution is correct!
Solution 2:
413, 413, 413
Verification:
(413 + 413 + 413) / 3 = 1239 / 3 ≈ 413
This solution is correct!
Solution 3:
1159, 5, 75
Verification:
(1159 + 5 + 75) / 3 = 1239 / 3 ≈ 413
This solution is correct!
Solution 4:
828, 123, 288
Verification:
(828 + 123 + 288) / 3 = 1239 / 3 ≈ 413
This solution is correct!
Solution 5:
432, 529, 278
Verification:
(432 + 529 + 278) / 3 = 1239 / 3 ≈ 413
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 1239 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.