What three numbers have an average of 703?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 703. This means if we add these three numbers together and divide by 3, we should get 703.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 703 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 703 * 3 = x + y + z
- So, the sum of our three numbers should be: 2109
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2109.
Solution 1:
703, 703, 703
Verification:
(703 + 703 + 703) / 3 = 2109 / 3 ≈ 703
This solution is correct!
Solution 2:
703, 703, 703
Verification:
(703 + 703 + 703) / 3 = 2109 / 3 ≈ 703
This solution is correct!
Solution 3:
503, 1135, 471
Verification:
(503 + 1135 + 471) / 3 = 2109 / 3 ≈ 703
This solution is correct!
Solution 4:
154, 1526, 429
Verification:
(154 + 1526 + 429) / 3 = 2109 / 3 ≈ 703
This solution is correct!
Solution 5:
932, 483, 694
Verification:
(932 + 483 + 694) / 3 = 2109 / 3 ≈ 703
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 2109 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.