What three numbers have an average of 940?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 940. This means if we add these three numbers together and divide by 3, we should get 940.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 940 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 940 * 3 = x + y + z
- So, the sum of our three numbers should be: 2820
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2820.
Solution 1:
940, 940, 940
Verification:
(940 + 940 + 940) / 3 = 2820 / 3 ≈ 940
This solution is correct!
Solution 2:
940, 940, 940
Verification:
(940 + 940 + 940) / 3 = 2820 / 3 ≈ 940
This solution is correct!
Solution 3:
44, 729, 2047
Verification:
(44 + 729 + 2047) / 3 = 2820 / 3 ≈ 940
This solution is correct!
Solution 4:
1847, 706, 267
Verification:
(1847 + 706 + 267) / 3 = 2820 / 3 ≈ 940
This solution is correct!
Solution 5:
2009, 181, 630
Verification:
(2009 + 181 + 630) / 3 = 2820 / 3 ≈ 940
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 2820 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.