What three numbers have an average of 478?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 478. This means if we add these three numbers together and divide by 3, we should get 478.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 478 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 478 * 3 = x + y + z
- So, the sum of our three numbers should be: 1434
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1434.
Solution 1:
478, 478, 478
Verification:
(478 + 478 + 478) / 3 = 1434 / 3 ≈ 478
This solution is correct!
Solution 2:
478, 478, 478
Verification:
(478 + 478 + 478) / 3 = 1434 / 3 ≈ 478
This solution is correct!
Solution 3:
1390, 7, 37
Verification:
(1390 + 7 + 37) / 3 = 1434 / 3 ≈ 478
This solution is correct!
Solution 4:
56, 282, 1096
Verification:
(56 + 282 + 1096) / 3 = 1434 / 3 ≈ 478
This solution is correct!
Solution 5:
1196, 33, 205
Verification:
(1196 + 33 + 205) / 3 = 1434 / 3 ≈ 478
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 1434 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.