What three numbers have an average of 811?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 811. This means if we add these three numbers together and divide by 3, we should get 811.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 811 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 811 * 3 = x + y + z
- So, the sum of our three numbers should be: 2433
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2433.
Solution 1:
811, 811, 811
Verification:
(811 + 811 + 811) / 3 = 2433 / 3 ≈ 811
This solution is correct!
Solution 2:
811, 811, 811
Verification:
(811 + 811 + 811) / 3 = 2433 / 3 ≈ 811
This solution is correct!
Solution 3:
1044, 800, 589
Verification:
(1044 + 800 + 589) / 3 = 2433 / 3 ≈ 811
This solution is correct!
Solution 4:
1954, 128, 351
Verification:
(1954 + 128 + 351) / 3 = 2433 / 3 ≈ 811
This solution is correct!
Solution 5:
1208, 118, 1107
Verification:
(1208 + 118 + 1107) / 3 = 2433 / 3 ≈ 811
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 2433 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.