What three numbers have an average of 314?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 314. This means if we add these three numbers together and divide by 3, we should get 314.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 314 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 314 * 3 = x + y + z
- So, the sum of our three numbers should be: 942
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 942.
Solution 1:
314, 314, 314
Verification:
(314 + 314 + 314) / 3 = 942 / 3 ≈ 314
This solution is correct!
Solution 2:
314, 314, 314
Verification:
(314 + 314 + 314) / 3 = 942 / 3 ≈ 314
This solution is correct!
Solution 3:
610, 251, 81
Verification:
(610 + 251 + 81) / 3 = 942 / 3 ≈ 314
This solution is correct!
Solution 4:
860, 52, 30
Verification:
(860 + 52 + 30) / 3 = 942 / 3 ≈ 314
This solution is correct!
Solution 5:
483, 167, 292
Verification:
(483 + 167 + 292) / 3 = 942 / 3 ≈ 314
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 942 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.