What three numbers have an average of 800?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 800. This means if we add these three numbers together and divide by 3, we should get 800.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 800 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 800 * 3 = x + y + z
- So, the sum of our three numbers should be: 2400
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2400.
Solution 1:
800, 800, 800
Verification:
(800 + 800 + 800) / 3 = 2400 / 3 ≈ 800
This solution is correct!
Solution 2:
800, 800, 800
Verification:
(800 + 800 + 800) / 3 = 2400 / 3 ≈ 800
This solution is correct!
Solution 3:
1077, 1249, 74
Verification:
(1077 + 1249 + 74) / 3 = 2400 / 3 ≈ 800
This solution is correct!
Solution 4:
2292, 5, 103
Verification:
(2292 + 5 + 103) / 3 = 2400 / 3 ≈ 800
This solution is correct!
Solution 5:
865, 1233, 302
Verification:
(865 + 1233 + 302) / 3 = 2400 / 3 ≈ 800
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 2400 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.