What three numbers have an average of 722?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 722. This means if we add these three numbers together and divide by 3, we should get 722.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 722 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 722 * 3 = x + y + z
- So, the sum of our three numbers should be: 2166
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2166.
Solution 1:
722, 722, 722
Verification:
(722 + 722 + 722) / 3 = 2166 / 3 ≈ 722
This solution is correct!
Solution 2:
722, 722, 722
Verification:
(722 + 722 + 722) / 3 = 2166 / 3 ≈ 722
This solution is correct!
Solution 3:
90, 873, 1203
Verification:
(90 + 873 + 1203) / 3 = 2166 / 3 ≈ 722
This solution is correct!
Solution 4:
1627, 250, 289
Verification:
(1627 + 250 + 289) / 3 = 2166 / 3 ≈ 722
This solution is correct!
Solution 5:
366, 658, 1142
Verification:
(366 + 658 + 1142) / 3 = 2166 / 3 ≈ 722
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 2166 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.