What three numbers have an average of 913?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 913. This means if we add these three numbers together and divide by 3, we should get 913.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 913 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 913 * 3 = x + y + z
- So, the sum of our three numbers should be: 2739
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2739.
Solution 1:
913, 913, 913
Verification:
(913 + 913 + 913) / 3 = 2739 / 3 ≈ 913
This solution is correct!
Solution 2:
913, 913, 913
Verification:
(913 + 913 + 913) / 3 = 2739 / 3 ≈ 913
This solution is correct!
Solution 3:
853, 1344, 542
Verification:
(853 + 1344 + 542) / 3 = 2739 / 3 ≈ 913
This solution is correct!
Solution 4:
884, 1223, 632
Verification:
(884 + 1223 + 632) / 3 = 2739 / 3 ≈ 913
This solution is correct!
Solution 5:
332, 742, 1665
Verification:
(332 + 742 + 1665) / 3 = 2739 / 3 ≈ 913
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 2739 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.