What three numbers have an average of 435?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 435. This means if we add these three numbers together and divide by 3, we should get 435.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 435 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 435 * 3 = x + y + z
- So, the sum of our three numbers should be: 1305
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1305.
Solution 1:
435, 435, 435
Verification:
(435 + 435 + 435) / 3 = 1305 / 3 ≈ 435
This solution is correct!
Solution 2:
435, 435, 435
Verification:
(435 + 435 + 435) / 3 = 1305 / 3 ≈ 435
This solution is correct!
Solution 3:
891, 244, 170
Verification:
(891 + 244 + 170) / 3 = 1305 / 3 ≈ 435
This solution is correct!
Solution 4:
591, 272, 442
Verification:
(591 + 272 + 442) / 3 = 1305 / 3 ≈ 435
This solution is correct!
Solution 5:
187, 283, 835
Verification:
(187 + 283 + 835) / 3 = 1305 / 3 ≈ 435
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 1305 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.