What three numbers have an average of 403?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 403. This means if we add these three numbers together and divide by 3, we should get 403.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 403 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 403 * 3 = x + y + z
- So, the sum of our three numbers should be: 1209
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1209.
Solution 1:
403, 403, 403
Verification:
(403 + 403 + 403) / 3 = 1209 / 3 ≈ 403
This solution is correct!
Solution 2:
403, 403, 403
Verification:
(403 + 403 + 403) / 3 = 1209 / 3 ≈ 403
This solution is correct!
Solution 3:
118, 556, 535
Verification:
(118 + 556 + 535) / 3 = 1209 / 3 ≈ 403
This solution is correct!
Solution 4:
319, 788, 102
Verification:
(319 + 788 + 102) / 3 = 1209 / 3 ≈ 403
This solution is correct!
Solution 5:
738, 316, 155
Verification:
(738 + 316 + 155) / 3 = 1209 / 3 ≈ 403
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 1209 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.