What three numbers have an average of 708?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 708. This means if we add these three numbers together and divide by 3, we should get 708.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 708 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 708 * 3 = x + y + z
- So, the sum of our three numbers should be: 2124
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2124.
Solution 1:
708, 708, 708
Verification:
(708 + 708 + 708) / 3 = 2124 / 3 ≈ 708
This solution is correct!
Solution 2:
708, 708, 708
Verification:
(708 + 708 + 708) / 3 = 2124 / 3 ≈ 708
This solution is correct!
Solution 3:
894, 354, 876
Verification:
(894 + 354 + 876) / 3 = 2124 / 3 ≈ 708
This solution is correct!
Solution 4:
1204, 775, 145
Verification:
(1204 + 775 + 145) / 3 = 2124 / 3 ≈ 708
This solution is correct!
Solution 5:
1439, 434, 251
Verification:
(1439 + 434 + 251) / 3 = 2124 / 3 ≈ 708
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 2124 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.