What three numbers have an average of 614?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 614. This means if we add these three numbers together and divide by 3, we should get 614.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 614 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 614 * 3 = x + y + z
- So, the sum of our three numbers should be: 1842
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1842.
Solution 1:
614, 614, 614
Verification:
(614 + 614 + 614) / 3 = 1842 / 3 ≈ 614
This solution is correct!
Solution 2:
614, 614, 614
Verification:
(614 + 614 + 614) / 3 = 1842 / 3 ≈ 614
This solution is correct!
Solution 3:
1655, 162, 25
Verification:
(1655 + 162 + 25) / 3 = 1842 / 3 ≈ 614
This solution is correct!
Solution 4:
1400, 34, 408
Verification:
(1400 + 34 + 408) / 3 = 1842 / 3 ≈ 614
This solution is correct!
Solution 5:
1565, 141, 136
Verification:
(1565 + 141 + 136) / 3 = 1842 / 3 ≈ 614
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 1842 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.