What three numbers have an average of 399?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 399. This means if we add these three numbers together and divide by 3, we should get 399.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 399 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 399 * 3 = x + y + z
- So, the sum of our three numbers should be: 1197
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1197.
Solution 1:
399, 399, 399
Verification:
(399 + 399 + 399) / 3 = 1197 / 3 ≈ 399
This solution is correct!
Solution 2:
399, 399, 399
Verification:
(399 + 399 + 399) / 3 = 1197 / 3 ≈ 399
This solution is correct!
Solution 3:
129, 352, 716
Verification:
(129 + 352 + 716) / 3 = 1197 / 3 ≈ 399
This solution is correct!
Solution 4:
854, 134, 209
Verification:
(854 + 134 + 209) / 3 = 1197 / 3 ≈ 399
This solution is correct!
Solution 5:
57, 450, 690
Verification:
(57 + 450 + 690) / 3 = 1197 / 3 ≈ 399
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 1197 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.