What three numbers have an average of 307?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 307. This means if we add these three numbers together and divide by 3, we should get 307.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 307 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 307 * 3 = x + y + z
- So, the sum of our three numbers should be: 921
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 921.
Solution 1:
307, 307, 307
Verification:
(307 + 307 + 307) / 3 = 921 / 3 ≈ 307
This solution is correct!
Solution 2:
307, 307, 307
Verification:
(307 + 307 + 307) / 3 = 921 / 3 ≈ 307
This solution is correct!
Solution 3:
90, 406, 425
Verification:
(90 + 406 + 425) / 3 = 921 / 3 ≈ 307
This solution is correct!
Solution 4:
720, 127, 74
Verification:
(720 + 127 + 74) / 3 = 921 / 3 ≈ 307
This solution is correct!
Solution 5:
787, 47, 87
Verification:
(787 + 47 + 87) / 3 = 921 / 3 ≈ 307
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 921 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.