What three numbers have an average of 400?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 400. This means if we add these three numbers together and divide by 3, we should get 400.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 400 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 400 * 3 = x + y + z
- So, the sum of our three numbers should be: 1200
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1200.
Solution 1:
400, 400, 400
Verification:
(400 + 400 + 400) / 3 = 1200 / 3 ≈ 400
This solution is correct!
Solution 2:
400, 400, 400
Verification:
(400 + 400 + 400) / 3 = 1200 / 3 ≈ 400
This solution is correct!
Solution 3:
197, 14, 989
Verification:
(197 + 14 + 989) / 3 = 1200 / 3 ≈ 400
This solution is correct!
Solution 4:
721, 408, 71
Verification:
(721 + 408 + 71) / 3 = 1200 / 3 ≈ 400
This solution is correct!
Solution 5:
1183, 3, 14
Verification:
(1183 + 3 + 14) / 3 = 1200 / 3 ≈ 400
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 1200 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.