What three numbers have an average of 743?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 743. This means if we add these three numbers together and divide by 3, we should get 743.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 743 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 743 * 3 = x + y + z
- So, the sum of our three numbers should be: 2229
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2229.
Solution 1:
743, 743, 743
Verification:
(743 + 743 + 743) / 3 = 2229 / 3 ≈ 743
This solution is correct!
Solution 2:
743, 743, 743
Verification:
(743 + 743 + 743) / 3 = 2229 / 3 ≈ 743
This solution is correct!
Solution 3:
149, 1925, 155
Verification:
(149 + 1925 + 155) / 3 = 2229 / 3 ≈ 743
This solution is correct!
Solution 4:
1426, 57, 746
Verification:
(1426 + 57 + 746) / 3 = 2229 / 3 ≈ 743
This solution is correct!
Solution 5:
2187, 25, 17
Verification:
(2187 + 25 + 17) / 3 = 2229 / 3 ≈ 743
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 2229 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.