What three numbers have an average of 472?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 472. This means if we add these three numbers together and divide by 3, we should get 472.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 472 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 472 * 3 = x + y + z
- So, the sum of our three numbers should be: 1416
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1416.
Solution 1:
472, 472, 472
Verification:
(472 + 472 + 472) / 3 = 1416 / 3 ≈ 472
This solution is correct!
Solution 2:
472, 472, 472
Verification:
(472 + 472 + 472) / 3 = 1416 / 3 ≈ 472
This solution is correct!
Solution 3:
369, 427, 620
Verification:
(369 + 427 + 620) / 3 = 1416 / 3 ≈ 472
This solution is correct!
Solution 4:
1290, 25, 101
Verification:
(1290 + 25 + 101) / 3 = 1416 / 3 ≈ 472
This solution is correct!
Solution 5:
558, 282, 576
Verification:
(558 + 282 + 576) / 3 = 1416 / 3 ≈ 472
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 1416 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.