What three numbers have an average of 450?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 450. This means if we add these three numbers together and divide by 3, we should get 450.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 450 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 450 * 3 = x + y + z
- So, the sum of our three numbers should be: 1350
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1350.
Solution 1:
450, 450, 450
Verification:
(450 + 450 + 450) / 3 = 1350 / 3 ≈ 450
This solution is correct!
Solution 2:
450, 450, 450
Verification:
(450 + 450 + 450) / 3 = 1350 / 3 ≈ 450
This solution is correct!
Solution 3:
1124, 211, 15
Verification:
(1124 + 211 + 15) / 3 = 1350 / 3 ≈ 450
This solution is correct!
Solution 4:
98, 1001, 251
Verification:
(98 + 1001 + 251) / 3 = 1350 / 3 ≈ 450
This solution is correct!
Solution 5:
706, 559, 85
Verification:
(706 + 559 + 85) / 3 = 1350 / 3 ≈ 450
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 1350 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.