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:
700, 185, 951
Verification:
(700 + 185 + 951) / 3 = 1836 / 3 ≈ 612
This solution is correct!
Solution 4:
1345, 223, 268
Verification:
(1345 + 223 + 268) / 3 = 1836 / 3 ≈ 612
This solution is correct!
Solution 5:
106, 1101, 629
Verification:
(106 + 1101 + 629) / 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.