What three numbers have an average of 745?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 745. This means if we add these three numbers together and divide by 3, we should get 745.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 745 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 745 * 3 = x + y + z
- So, the sum of our three numbers should be: 2235
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2235.
Solution 1:
745, 745, 745
Verification:
(745 + 745 + 745) / 3 = 2235 / 3 ≈ 745
This solution is correct!
Solution 2:
745, 745, 745
Verification:
(745 + 745 + 745) / 3 = 2235 / 3 ≈ 745
This solution is correct!
Solution 3:
311, 369, 1555
Verification:
(311 + 369 + 1555) / 3 = 2235 / 3 ≈ 745
This solution is correct!
Solution 4:
1189, 494, 552
Verification:
(1189 + 494 + 552) / 3 = 2235 / 3 ≈ 745
This solution is correct!
Solution 5:
1088, 288, 859
Verification:
(1088 + 288 + 859) / 3 = 2235 / 3 ≈ 745
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 2235 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.