What three numbers have an average of 878?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 878. This means if we add these three numbers together and divide by 3, we should get 878.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 878 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 878 * 3 = x + y + z
- So, the sum of our three numbers should be: 2634
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2634.
Solution 1:
878, 878, 878
Verification:
(878 + 878 + 878) / 3 = 2634 / 3 ≈ 878
This solution is correct!
Solution 2:
878, 878, 878
Verification:
(878 + 878 + 878) / 3 = 2634 / 3 ≈ 878
This solution is correct!
Solution 3:
1053, 490, 1091
Verification:
(1053 + 490 + 1091) / 3 = 2634 / 3 ≈ 878
This solution is correct!
Solution 4:
1579, 960, 95
Verification:
(1579 + 960 + 95) / 3 = 2634 / 3 ≈ 878
This solution is correct!
Solution 5:
1278, 478, 878
Verification:
(1278 + 478 + 878) / 3 = 2634 / 3 ≈ 878
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 2634 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.