What three numbers have an average of 677?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 677. This means if we add these three numbers together and divide by 3, we should get 677.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 677 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 677 * 3 = x + y + z
- So, the sum of our three numbers should be: 2031
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2031.
Solution 1:
677, 677, 677
Verification:
(677 + 677 + 677) / 3 = 2031 / 3 ≈ 677
This solution is correct!
Solution 2:
677, 677, 677
Verification:
(677 + 677 + 677) / 3 = 2031 / 3 ≈ 677
This solution is correct!
Solution 3:
1224, 573, 234
Verification:
(1224 + 573 + 234) / 3 = 2031 / 3 ≈ 677
This solution is correct!
Solution 4:
131, 597, 1303
Verification:
(131 + 597 + 1303) / 3 = 2031 / 3 ≈ 677
This solution is correct!
Solution 5:
273, 1327, 431
Verification:
(273 + 1327 + 431) / 3 = 2031 / 3 ≈ 677
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 2031 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.