What three numbers have an average of 780?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 780. This means if we add these three numbers together and divide by 3, we should get 780.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 780 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 780 * 3 = x + y + z
- So, the sum of our three numbers should be: 2340
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2340.
Solution 1:
780, 780, 780
Verification:
(780 + 780 + 780) / 3 = 2340 / 3 ≈ 780
This solution is correct!
Solution 2:
780, 780, 780
Verification:
(780 + 780 + 780) / 3 = 2340 / 3 ≈ 780
This solution is correct!
Solution 3:
2027, 227, 86
Verification:
(2027 + 227 + 86) / 3 = 2340 / 3 ≈ 780
This solution is correct!
Solution 4:
1352, 613, 375
Verification:
(1352 + 613 + 375) / 3 = 2340 / 3 ≈ 780
This solution is correct!
Solution 5:
684, 309, 1347
Verification:
(684 + 309 + 1347) / 3 = 2340 / 3 ≈ 780
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 2340 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.