What three numbers have an average of 789?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 789. This means if we add these three numbers together and divide by 3, we should get 789.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 789 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 789 * 3 = x + y + z
- So, the sum of our three numbers should be: 2367
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2367.
Solution 1:
789, 789, 789
Verification:
(789 + 789 + 789) / 3 = 2367 / 3 ≈ 789
This solution is correct!
Solution 2:
789, 789, 789
Verification:
(789 + 789 + 789) / 3 = 2367 / 3 ≈ 789
This solution is correct!
Solution 3:
553, 1005, 809
Verification:
(553 + 1005 + 809) / 3 = 2367 / 3 ≈ 789
This solution is correct!
Solution 4:
818, 876, 673
Verification:
(818 + 876 + 673) / 3 = 2367 / 3 ≈ 789
This solution is correct!
Solution 5:
99, 1823, 445
Verification:
(99 + 1823 + 445) / 3 = 2367 / 3 ≈ 789
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 2367 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.