What three numbers have an average of 876?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 876. This means if we add these three numbers together and divide by 3, we should get 876.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 876 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 876 * 3 = x + y + z
- So, the sum of our three numbers should be: 2628
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2628.
Solution 1:
876, 876, 876
Verification:
(876 + 876 + 876) / 3 = 2628 / 3 ≈ 876
This solution is correct!
Solution 2:
876, 876, 876
Verification:
(876 + 876 + 876) / 3 = 2628 / 3 ≈ 876
This solution is correct!
Solution 3:
499, 311, 1818
Verification:
(499 + 311 + 1818) / 3 = 2628 / 3 ≈ 876
This solution is correct!
Solution 4:
284, 78, 2266
Verification:
(284 + 78 + 2266) / 3 = 2628 / 3 ≈ 876
This solution is correct!
Solution 5:
2260, 174, 194
Verification:
(2260 + 174 + 194) / 3 = 2628 / 3 ≈ 876
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 2628 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.