What three numbers have an average of 310?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 310. This means if we add these three numbers together and divide by 3, we should get 310.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 310 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 310 * 3 = x + y + z
- So, the sum of our three numbers should be: 930
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 930.
Solution 1:
310, 310, 310
Verification:
(310 + 310 + 310) / 3 = 930 / 3 ≈ 310
This solution is correct!
Solution 2:
310, 310, 310
Verification:
(310 + 310 + 310) / 3 = 930 / 3 ≈ 310
This solution is correct!
Solution 3:
656, 96, 178
Verification:
(656 + 96 + 178) / 3 = 930 / 3 ≈ 310
This solution is correct!
Solution 4:
531, 241, 158
Verification:
(531 + 241 + 158) / 3 = 930 / 3 ≈ 310
This solution is correct!
Solution 5:
676, 195, 59
Verification:
(676 + 195 + 59) / 3 = 930 / 3 ≈ 310
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 930 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.