What three numbers have an average of 788?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 788. This means if we add these three numbers together and divide by 3, we should get 788.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 788 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 788 * 3 = x + y + z
- So, the sum of our three numbers should be: 2364
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2364.
Solution 1:
788, 788, 788
Verification:
(788 + 788 + 788) / 3 = 2364 / 3 ≈ 788
This solution is correct!
Solution 2:
788, 788, 788
Verification:
(788 + 788 + 788) / 3 = 2364 / 3 ≈ 788
This solution is correct!
Solution 3:
1264, 194, 906
Verification:
(1264 + 194 + 906) / 3 = 2364 / 3 ≈ 788
This solution is correct!
Solution 4:
1976, 244, 144
Verification:
(1976 + 244 + 144) / 3 = 2364 / 3 ≈ 788
This solution is correct!
Solution 5:
2218, 118, 28
Verification:
(2218 + 118 + 28) / 3 = 2364 / 3 ≈ 788
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 2364 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.