What three numbers have an average of 410?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 410. This means if we add these three numbers together and divide by 3, we should get 410.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 410 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 410 * 3 = x + y + z
- So, the sum of our three numbers should be: 1230
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1230.
Solution 1:
410, 410, 410
Verification:
(410 + 410 + 410) / 3 = 1230 / 3 ≈ 410
This solution is correct!
Solution 2:
410, 410, 410
Verification:
(410 + 410 + 410) / 3 = 1230 / 3 ≈ 410
This solution is correct!
Solution 3:
524, 518, 188
Verification:
(524 + 518 + 188) / 3 = 1230 / 3 ≈ 410
This solution is correct!
Solution 4:
106, 312, 812
Verification:
(106 + 312 + 812) / 3 = 1230 / 3 ≈ 410
This solution is correct!
Solution 5:
509, 152, 569
Verification:
(509 + 152 + 569) / 3 = 1230 / 3 ≈ 410
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 1230 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.