What three numbers have an average of 477?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 477. This means if we add these three numbers together and divide by 3, we should get 477.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 477 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 477 * 3 = x + y + z
- So, the sum of our three numbers should be: 1431
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1431.
Solution 1:
477, 477, 477
Verification:
(477 + 477 + 477) / 3 = 1431 / 3 ≈ 477
This solution is correct!
Solution 2:
477, 477, 477
Verification:
(477 + 477 + 477) / 3 = 1431 / 3 ≈ 477
This solution is correct!
Solution 3:
614, 166, 651
Verification:
(614 + 166 + 651) / 3 = 1431 / 3 ≈ 477
This solution is correct!
Solution 4:
615, 59, 757
Verification:
(615 + 59 + 757) / 3 = 1431 / 3 ≈ 477
This solution is correct!
Solution 5:
912, 374, 145
Verification:
(912 + 374 + 145) / 3 = 1431 / 3 ≈ 477
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 1431 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.