What three numbers have an average of 733?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 733. This means if we add these three numbers together and divide by 3, we should get 733.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 733 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 733 * 3 = x + y + z
- So, the sum of our three numbers should be: 2199
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2199.
Solution 1:
733, 733, 733
Verification:
(733 + 733 + 733) / 3 = 2199 / 3 ≈ 733
This solution is correct!
Solution 2:
733, 733, 733
Verification:
(733 + 733 + 733) / 3 = 2199 / 3 ≈ 733
This solution is correct!
Solution 3:
2197, 1, 1
Verification:
(2197 + 1 + 1) / 3 = 2199 / 3 ≈ 733
This solution is correct!
Solution 4:
835, 86, 1278
Verification:
(835 + 86 + 1278) / 3 = 2199 / 3 ≈ 733
This solution is correct!
Solution 5:
2022, 38, 139
Verification:
(2022 + 38 + 139) / 3 = 2199 / 3 ≈ 733
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 2199 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.