What three numbers have an average of 613?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 613. This means if we add these three numbers together and divide by 3, we should get 613.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 613 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 613 * 3 = x + y + z
- So, the sum of our three numbers should be: 1839
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1839.
Solution 1:
613, 613, 613
Verification:
(613 + 613 + 613) / 3 = 1839 / 3 ≈ 613
This solution is correct!
Solution 2:
613, 613, 613
Verification:
(613 + 613 + 613) / 3 = 1839 / 3 ≈ 613
This solution is correct!
Solution 3:
1831, 5, 3
Verification:
(1831 + 5 + 3) / 3 = 1839 / 3 ≈ 613
This solution is correct!
Solution 4:
1154, 608, 77
Verification:
(1154 + 608 + 77) / 3 = 1839 / 3 ≈ 613
This solution is correct!
Solution 5:
849, 888, 102
Verification:
(849 + 888 + 102) / 3 = 1839 / 3 ≈ 613
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 1839 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.