What three numbers have an average of 790?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 790. This means if we add these three numbers together and divide by 3, we should get 790.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 790 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 790 * 3 = x + y + z
- So, the sum of our three numbers should be: 2370
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2370.
Solution 1:
790, 790, 790
Verification:
(790 + 790 + 790) / 3 = 2370 / 3 ≈ 790
This solution is correct!
Solution 2:
790, 790, 790
Verification:
(790 + 790 + 790) / 3 = 2370 / 3 ≈ 790
This solution is correct!
Solution 3:
1900, 419, 51
Verification:
(1900 + 419 + 51) / 3 = 2370 / 3 ≈ 790
This solution is correct!
Solution 4:
1094, 95, 1181
Verification:
(1094 + 95 + 1181) / 3 = 2370 / 3 ≈ 790
This solution is correct!
Solution 5:
1718, 77, 575
Verification:
(1718 + 77 + 575) / 3 = 2370 / 3 ≈ 790
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 2370 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.