What three numbers have an average of 894?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 894. This means if we add these three numbers together and divide by 3, we should get 894.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 894 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 894 * 3 = x + y + z
- So, the sum of our three numbers should be: 2682
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2682.
Solution 1:
894, 894, 894
Verification:
(894 + 894 + 894) / 3 = 2682 / 3 ≈ 894
This solution is correct!
Solution 2:
894, 894, 894
Verification:
(894 + 894 + 894) / 3 = 2682 / 3 ≈ 894
This solution is correct!
Solution 3:
508, 716, 1458
Verification:
(508 + 716 + 1458) / 3 = 2682 / 3 ≈ 894
This solution is correct!
Solution 4:
1143, 731, 808
Verification:
(1143 + 731 + 808) / 3 = 2682 / 3 ≈ 894
This solution is correct!
Solution 5:
1008, 1192, 482
Verification:
(1008 + 1192 + 482) / 3 = 2682 / 3 ≈ 894
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 2682 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.