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:
12, 2141, 280
Verification:
(12 + 2141 + 280) / 3 = 2433 / 3 ≈ 811
This solution is correct!
Solution 4:
2353, 3, 77
Verification:
(2353 + 3 + 77) / 3 = 2433 / 3 ≈ 811
This solution is correct!
Solution 5:
1043, 53, 1337
Verification:
(1043 + 53 + 1337) / 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.