What three numbers have an average of 801?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 801. This means if we add these three numbers together and divide by 3, we should get 801.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 801 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 801 * 3 = x + y + z
- So, the sum of our three numbers should be: 2403
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2403.
Solution 1:
801, 801, 801
Verification:
(801 + 801 + 801) / 3 = 2403 / 3 ≈ 801
This solution is correct!
Solution 2:
801, 801, 801
Verification:
(801 + 801 + 801) / 3 = 2403 / 3 ≈ 801
This solution is correct!
Solution 3:
1653, 284, 466
Verification:
(1653 + 284 + 466) / 3 = 2403 / 3 ≈ 801
This solution is correct!
Solution 4:
1133, 444, 826
Verification:
(1133 + 444 + 826) / 3 = 2403 / 3 ≈ 801
This solution is correct!
Solution 5:
966, 760, 677
Verification:
(966 + 760 + 677) / 3 = 2403 / 3 ≈ 801
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 2403 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.