What three numbers have an average of 488?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 488. This means if we add these three numbers together and divide by 3, we should get 488.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 488 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 488 * 3 = x + y + z
- So, the sum of our three numbers should be: 1464
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1464.
Solution 1:
488, 488, 488
Verification:
(488 + 488 + 488) / 3 = 1464 / 3 ≈ 488
This solution is correct!
Solution 2:
488, 488, 488
Verification:
(488 + 488 + 488) / 3 = 1464 / 3 ≈ 488
This solution is correct!
Solution 3:
91, 838, 535
Verification:
(91 + 838 + 535) / 3 = 1464 / 3 ≈ 488
This solution is correct!
Solution 4:
1292, 145, 27
Verification:
(1292 + 145 + 27) / 3 = 1464 / 3 ≈ 488
This solution is correct!
Solution 5:
1254, 101, 109
Verification:
(1254 + 101 + 109) / 3 = 1464 / 3 ≈ 488
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 1464 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.