What three numbers have an average of 489?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 489. This means if we add these three numbers together and divide by 3, we should get 489.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 489 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 489 * 3 = x + y + z
- So, the sum of our three numbers should be: 1467
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1467.
Solution 1:
489, 489, 489
Verification:
(489 + 489 + 489) / 3 = 1467 / 3 ≈ 489
This solution is correct!
Solution 2:
489, 489, 489
Verification:
(489 + 489 + 489) / 3 = 1467 / 3 ≈ 489
This solution is correct!
Solution 3:
426, 200, 841
Verification:
(426 + 200 + 841) / 3 = 1467 / 3 ≈ 489
This solution is correct!
Solution 4:
1310, 119, 38
Verification:
(1310 + 119 + 38) / 3 = 1467 / 3 ≈ 489
This solution is correct!
Solution 5:
1142, 9, 316
Verification:
(1142 + 9 + 316) / 3 = 1467 / 3 ≈ 489
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 1467 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.