What three numbers have an average of 470?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 470. This means if we add these three numbers together and divide by 3, we should get 470.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 470 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 470 * 3 = x + y + z
- So, the sum of our three numbers should be: 1410
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1410.
Solution 1:
470, 470, 470
Verification:
(470 + 470 + 470) / 3 = 1410 / 3 ≈ 470
This solution is correct!
Solution 2:
470, 470, 470
Verification:
(470 + 470 + 470) / 3 = 1410 / 3 ≈ 470
This solution is correct!
Solution 3:
6, 1009, 395
Verification:
(6 + 1009 + 395) / 3 = 1410 / 3 ≈ 470
This solution is correct!
Solution 4:
896, 79, 435
Verification:
(896 + 79 + 435) / 3 = 1410 / 3 ≈ 470
This solution is correct!
Solution 5:
418, 912, 80
Verification:
(418 + 912 + 80) / 3 = 1410 / 3 ≈ 470
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 1410 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.