What three numbers have an average of 340?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 340. This means if we add these three numbers together and divide by 3, we should get 340.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 340 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 340 * 3 = x + y + z
- So, the sum of our three numbers should be: 1020
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1020.
Solution 1:
340, 340, 340
Verification:
(340 + 340 + 340) / 3 = 1020 / 3 ≈ 340
This solution is correct!
Solution 2:
340, 340, 340
Verification:
(340 + 340 + 340) / 3 = 1020 / 3 ≈ 340
This solution is correct!
Solution 3:
870, 15, 135
Verification:
(870 + 15 + 135) / 3 = 1020 / 3 ≈ 340
This solution is correct!
Solution 4:
906, 76, 38
Verification:
(906 + 76 + 38) / 3 = 1020 / 3 ≈ 340
This solution is correct!
Solution 5:
693, 62, 265
Verification:
(693 + 62 + 265) / 3 = 1020 / 3 ≈ 340
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 1020 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.