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:
1225, 1021, 157
Verification:
(1225 + 1021 + 157) / 3 = 2403 / 3 ≈ 801
This solution is correct!
Solution 4:
2212, 107, 84
Verification:
(2212 + 107 + 84) / 3 = 2403 / 3 ≈ 801
This solution is correct!
Solution 5:
2059, 149, 195
Verification:
(2059 + 149 + 195) / 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.