What three numbers have an average of 785?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 785. This means if we add these three numbers together and divide by 3, we should get 785.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 785 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 785 * 3 = x + y + z
- So, the sum of our three numbers should be: 2355
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2355.
Solution 1:
785, 785, 785
Verification:
(785 + 785 + 785) / 3 = 2355 / 3 ≈ 785
This solution is correct!
Solution 2:
785, 785, 785
Verification:
(785 + 785 + 785) / 3 = 2355 / 3 ≈ 785
This solution is correct!
Solution 3:
1501, 31, 823
Verification:
(1501 + 31 + 823) / 3 = 2355 / 3 ≈ 785
This solution is correct!
Solution 4:
2231, 44, 80
Verification:
(2231 + 44 + 80) / 3 = 2355 / 3 ≈ 785
This solution is correct!
Solution 5:
1843, 373, 139
Verification:
(1843 + 373 + 139) / 3 = 2355 / 3 ≈ 785
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 2355 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.