What three numbers have an average of 496?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 496. This means if we add these three numbers together and divide by 3, we should get 496.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 496 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 496 * 3 = x + y + z
- So, the sum of our three numbers should be: 1488
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1488.
Solution 1:
496, 496, 496
Verification:
(496 + 496 + 496) / 3 = 1488 / 3 ≈ 496
This solution is correct!
Solution 2:
496, 496, 496
Verification:
(496 + 496 + 496) / 3 = 1488 / 3 ≈ 496
This solution is correct!
Solution 3:
804, 681, 3
Verification:
(804 + 681 + 3) / 3 = 1488 / 3 ≈ 496
This solution is correct!
Solution 4:
1164, 180, 144
Verification:
(1164 + 180 + 144) / 3 = 1488 / 3 ≈ 496
This solution is correct!
Solution 5:
511, 457, 520
Verification:
(511 + 457 + 520) / 3 = 1488 / 3 ≈ 496
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 1488 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.