What three numbers have an average of 810?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 810. This means if we add these three numbers together and divide by 3, we should get 810.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 810 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 810 * 3 = x + y + z
- So, the sum of our three numbers should be: 2430
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2430.
Solution 1:
810, 810, 810
Verification:
(810 + 810 + 810) / 3 = 2430 / 3 ≈ 810
This solution is correct!
Solution 2:
810, 810, 810
Verification:
(810 + 810 + 810) / 3 = 2430 / 3 ≈ 810
This solution is correct!
Solution 3:
970, 248, 1212
Verification:
(970 + 248 + 1212) / 3 = 2430 / 3 ≈ 810
This solution is correct!
Solution 4:
441, 409, 1580
Verification:
(441 + 409 + 1580) / 3 = 2430 / 3 ≈ 810
This solution is correct!
Solution 5:
228, 1994, 208
Verification:
(228 + 1994 + 208) / 3 = 2430 / 3 ≈ 810
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 2430 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.