What three numbers have an average of 809?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 809. This means if we add these three numbers together and divide by 3, we should get 809.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 809 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 809 * 3 = x + y + z
- So, the sum of our three numbers should be: 2427
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2427.
Solution 1:
809, 809, 809
Verification:
(809 + 809 + 809) / 3 = 2427 / 3 ≈ 809
This solution is correct!
Solution 2:
809, 809, 809
Verification:
(809 + 809 + 809) / 3 = 2427 / 3 ≈ 809
This solution is correct!
Solution 3:
801, 926, 700
Verification:
(801 + 926 + 700) / 3 = 2427 / 3 ≈ 809
This solution is correct!
Solution 4:
962, 507, 958
Verification:
(962 + 507 + 958) / 3 = 2427 / 3 ≈ 809
This solution is correct!
Solution 5:
270, 1853, 304
Verification:
(270 + 1853 + 304) / 3 = 2427 / 3 ≈ 809
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 2427 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.