What three numbers have an average of 419?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 419. This means if we add these three numbers together and divide by 3, we should get 419.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 419 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 419 * 3 = x + y + z
- So, the sum of our three numbers should be: 1257
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1257.
Solution 1:
419, 419, 419
Verification:
(419 + 419 + 419) / 3 = 1257 / 3 ≈ 419
This solution is correct!
Solution 2:
419, 419, 419
Verification:
(419 + 419 + 419) / 3 = 1257 / 3 ≈ 419
This solution is correct!
Solution 3:
275, 676, 306
Verification:
(275 + 676 + 306) / 3 = 1257 / 3 ≈ 419
This solution is correct!
Solution 4:
544, 439, 274
Verification:
(544 + 439 + 274) / 3 = 1257 / 3 ≈ 419
This solution is correct!
Solution 5:
934, 298, 25
Verification:
(934 + 298 + 25) / 3 = 1257 / 3 ≈ 419
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 1257 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.