What three numbers have an average of 868?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 868. This means if we add these three numbers together and divide by 3, we should get 868.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 868 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 868 * 3 = x + y + z
- So, the sum of our three numbers should be: 2604
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2604.
Solution 1:
868, 868, 868
Verification:
(868 + 868 + 868) / 3 = 2604 / 3 ≈ 868
This solution is correct!
Solution 2:
868, 868, 868
Verification:
(868 + 868 + 868) / 3 = 2604 / 3 ≈ 868
This solution is correct!
Solution 3:
464, 1131, 1009
Verification:
(464 + 1131 + 1009) / 3 = 2604 / 3 ≈ 868
This solution is correct!
Solution 4:
252, 1128, 1224
Verification:
(252 + 1128 + 1224) / 3 = 2604 / 3 ≈ 868
This solution is correct!
Solution 5:
664, 1747, 193
Verification:
(664 + 1747 + 193) / 3 = 2604 / 3 ≈ 868
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 2604 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.