What three numbers have an average of 383?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 383. This means if we add these three numbers together and divide by 3, we should get 383.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 383 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 383 * 3 = x + y + z
- So, the sum of our three numbers should be: 1149
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1149.
Solution 1:
383, 383, 383
Verification:
(383 + 383 + 383) / 3 = 1149 / 3 ≈ 383
This solution is correct!
Solution 2:
383, 383, 383
Verification:
(383 + 383 + 383) / 3 = 1149 / 3 ≈ 383
This solution is correct!
Solution 3:
141, 696, 312
Verification:
(141 + 696 + 312) / 3 = 1149 / 3 ≈ 383
This solution is correct!
Solution 4:
1106, 6, 37
Verification:
(1106 + 6 + 37) / 3 = 1149 / 3 ≈ 383
This solution is correct!
Solution 5:
591, 255, 303
Verification:
(591 + 255 + 303) / 3 = 1149 / 3 ≈ 383
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 1149 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.