What three numbers have an average of 946?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 946. This means if we add these three numbers together and divide by 3, we should get 946.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 946 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 946 * 3 = x + y + z
- So, the sum of our three numbers should be: 2838
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2838.
Solution 1:
946, 946, 946
Verification:
(946 + 946 + 946) / 3 = 2838 / 3 ≈ 946
This solution is correct!
Solution 2:
946, 946, 946
Verification:
(946 + 946 + 946) / 3 = 2838 / 3 ≈ 946
This solution is correct!
Solution 3:
509, 1163, 1166
Verification:
(509 + 1163 + 1166) / 3 = 2838 / 3 ≈ 946
This solution is correct!
Solution 4:
2448, 266, 124
Verification:
(2448 + 266 + 124) / 3 = 2838 / 3 ≈ 946
This solution is correct!
Solution 5:
2353, 280, 205
Verification:
(2353 + 280 + 205) / 3 = 2838 / 3 ≈ 946
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 2838 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.