What three numbers have an average of 484?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 484. This means if we add these three numbers together and divide by 3, we should get 484.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 484 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 484 * 3 = x + y + z
- So, the sum of our three numbers should be: 1452
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1452.
Solution 1:
484, 484, 484
Verification:
(484 + 484 + 484) / 3 = 1452 / 3 ≈ 484
This solution is correct!
Solution 2:
484, 484, 484
Verification:
(484 + 484 + 484) / 3 = 1452 / 3 ≈ 484
This solution is correct!
Solution 3:
343, 1011, 98
Verification:
(343 + 1011 + 98) / 3 = 1452 / 3 ≈ 484
This solution is correct!
Solution 4:
533, 908, 11
Verification:
(533 + 908 + 11) / 3 = 1452 / 3 ≈ 484
This solution is correct!
Solution 5:
1175, 132, 145
Verification:
(1175 + 132 + 145) / 3 = 1452 / 3 ≈ 484
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 1452 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.