What three numbers have an average of 445?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 445. This means if we add these three numbers together and divide by 3, we should get 445.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 445 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 445 * 3 = x + y + z
- So, the sum of our three numbers should be: 1335
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1335.
Solution 1:
445, 445, 445
Verification:
(445 + 445 + 445) / 3 = 1335 / 3 ≈ 445
This solution is correct!
Solution 2:
445, 445, 445
Verification:
(445 + 445 + 445) / 3 = 1335 / 3 ≈ 445
This solution is correct!
Solution 3:
640, 225, 470
Verification:
(640 + 225 + 470) / 3 = 1335 / 3 ≈ 445
This solution is correct!
Solution 4:
431, 435, 469
Verification:
(431 + 435 + 469) / 3 = 1335 / 3 ≈ 445
This solution is correct!
Solution 5:
644, 394, 297
Verification:
(644 + 394 + 297) / 3 = 1335 / 3 ≈ 445
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 1335 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.