What three numbers have an average of 700?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 700. This means if we add these three numbers together and divide by 3, we should get 700.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 700 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 700 * 3 = x + y + z
- So, the sum of our three numbers should be: 2100
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2100.
Solution 1:
700, 700, 700
Verification:
(700 + 700 + 700) / 3 = 2100 / 3 ≈ 700
This solution is correct!
Solution 2:
700, 700, 700
Verification:
(700 + 700 + 700) / 3 = 2100 / 3 ≈ 700
This solution is correct!
Solution 3:
38, 872, 1190
Verification:
(38 + 872 + 1190) / 3 = 2100 / 3 ≈ 700
This solution is correct!
Solution 4:
360, 417, 1323
Verification:
(360 + 417 + 1323) / 3 = 2100 / 3 ≈ 700
This solution is correct!
Solution 5:
1509, 22, 569
Verification:
(1509 + 22 + 569) / 3 = 2100 / 3 ≈ 700
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 2100 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.