What three numbers have an average of 734?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 734. This means if we add these three numbers together and divide by 3, we should get 734.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 734 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 734 * 3 = x + y + z
- So, the sum of our three numbers should be: 2202
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2202.
Solution 1:
734, 734, 734
Verification:
(734 + 734 + 734) / 3 = 2202 / 3 ≈ 734
This solution is correct!
Solution 2:
734, 734, 734
Verification:
(734 + 734 + 734) / 3 = 2202 / 3 ≈ 734
This solution is correct!
Solution 3:
806, 1236, 160
Verification:
(806 + 1236 + 160) / 3 = 2202 / 3 ≈ 734
This solution is correct!
Solution 4:
730, 738, 734
Verification:
(730 + 738 + 734) / 3 = 2202 / 3 ≈ 734
This solution is correct!
Solution 5:
2147, 21, 34
Verification:
(2147 + 21 + 34) / 3 = 2202 / 3 ≈ 734
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 2202 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.