What three numbers have an average of 612?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 612. This means if we add these three numbers together and divide by 3, we should get 612.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 612 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 612 * 3 = x + y + z
- So, the sum of our three numbers should be: 1836
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1836.
Solution 1:
612, 612, 612
Verification:
(612 + 612 + 612) / 3 = 1836 / 3 ≈ 612
This solution is correct!
Solution 2:
612, 612, 612
Verification:
(612 + 612 + 612) / 3 = 1836 / 3 ≈ 612
This solution is correct!
Solution 3:
14, 1087, 735
Verification:
(14 + 1087 + 735) / 3 = 1836 / 3 ≈ 612
This solution is correct!
Solution 4:
301, 787, 748
Verification:
(301 + 787 + 748) / 3 = 1836 / 3 ≈ 612
This solution is correct!
Solution 5:
1067, 554, 215
Verification:
(1067 + 554 + 215) / 3 = 1836 / 3 ≈ 612
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 1836 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.