What three numbers have an average of 316?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 316. This means if we add these three numbers together and divide by 3, we should get 316.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 316 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 316 * 3 = x + y + z
- So, the sum of our three numbers should be: 948
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 948.
Solution 1:
316, 316, 316
Verification:
(316 + 316 + 316) / 3 = 948 / 3 ≈ 316
This solution is correct!
Solution 2:
316, 316, 316
Verification:
(316 + 316 + 316) / 3 = 948 / 3 ≈ 316
This solution is correct!
Solution 3:
174, 263, 511
Verification:
(174 + 263 + 511) / 3 = 948 / 3 ≈ 316
This solution is correct!
Solution 4:
472, 301, 175
Verification:
(472 + 301 + 175) / 3 = 948 / 3 ≈ 316
This solution is correct!
Solution 5:
793, 145, 10
Verification:
(793 + 145 + 10) / 3 = 948 / 3 ≈ 316
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 948 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.