What three numbers have an average of 469?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 469. This means if we add these three numbers together and divide by 3, we should get 469.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 469 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 469 * 3 = x + y + z
- So, the sum of our three numbers should be: 1407
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1407.
Solution 1:
469, 469, 469
Verification:
(469 + 469 + 469) / 3 = 1407 / 3 ≈ 469
This solution is correct!
Solution 2:
469, 469, 469
Verification:
(469 + 469 + 469) / 3 = 1407 / 3 ≈ 469
This solution is correct!
Solution 3:
713, 121, 573
Verification:
(713 + 121 + 573) / 3 = 1407 / 3 ≈ 469
This solution is correct!
Solution 4:
815, 275, 317
Verification:
(815 + 275 + 317) / 3 = 1407 / 3 ≈ 469
This solution is correct!
Solution 5:
804, 298, 305
Verification:
(804 + 298 + 305) / 3 = 1407 / 3 ≈ 469
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 1407 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.