What three numbers have an average of 735?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 735. This means if we add these three numbers together and divide by 3, we should get 735.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 735 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 735 * 3 = x + y + z
- So, the sum of our three numbers should be: 2205
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2205.
Solution 1:
735, 735, 735
Verification:
(735 + 735 + 735) / 3 = 2205 / 3 ≈ 735
This solution is correct!
Solution 2:
735, 735, 735
Verification:
(735 + 735 + 735) / 3 = 2205 / 3 ≈ 735
This solution is correct!
Solution 3:
49, 1537, 619
Verification:
(49 + 1537 + 619) / 3 = 2205 / 3 ≈ 735
This solution is correct!
Solution 4:
155, 765, 1285
Verification:
(155 + 765 + 1285) / 3 = 2205 / 3 ≈ 735
This solution is correct!
Solution 5:
241, 1819, 145
Verification:
(241 + 1819 + 145) / 3 = 2205 / 3 ≈ 735
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 2205 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.