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:
1360, 224, 621
Verification:
(1360 + 224 + 621) / 3 = 2205 / 3 ≈ 735
This solution is correct!
Solution 4:
1595, 465, 145
Verification:
(1595 + 465 + 145) / 3 = 2205 / 3 ≈ 735
This solution is correct!
Solution 5:
1284, 692, 229
Verification:
(1284 + 692 + 229) / 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.