What three numbers have an average of 704?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 704. This means if we add these three numbers together and divide by 3, we should get 704.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 704 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 704 * 3 = x + y + z
- So, the sum of our three numbers should be: 2112
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2112.
Solution 1:
704, 704, 704
Verification:
(704 + 704 + 704) / 3 = 2112 / 3 ≈ 704
This solution is correct!
Solution 2:
704, 704, 704
Verification:
(704 + 704 + 704) / 3 = 2112 / 3 ≈ 704
This solution is correct!
Solution 3:
1819, 175, 118
Verification:
(1819 + 175 + 118) / 3 = 2112 / 3 ≈ 704
This solution is correct!
Solution 4:
1408, 182, 522
Verification:
(1408 + 182 + 522) / 3 = 2112 / 3 ≈ 704
This solution is correct!
Solution 5:
2068, 3, 41
Verification:
(2068 + 3 + 41) / 3 = 2112 / 3 ≈ 704
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 2112 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.