What three numbers have an average of 359?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 359. This means if we add these three numbers together and divide by 3, we should get 359.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 359 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 359 * 3 = x + y + z
- So, the sum of our three numbers should be: 1077
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1077.
Solution 1:
359, 359, 359
Verification:
(359 + 359 + 359) / 3 = 1077 / 3 ≈ 359
This solution is correct!
Solution 2:
359, 359, 359
Verification:
(359 + 359 + 359) / 3 = 1077 / 3 ≈ 359
This solution is correct!
Solution 3:
458, 500, 119
Verification:
(458 + 500 + 119) / 3 = 1077 / 3 ≈ 359
This solution is correct!
Solution 4:
388, 605, 84
Verification:
(388 + 605 + 84) / 3 = 1077 / 3 ≈ 359
This solution is correct!
Solution 5:
540, 331, 206
Verification:
(540 + 331 + 206) / 3 = 1077 / 3 ≈ 359
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 1077 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.