What three numbers have an average of 749?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 749. This means if we add these three numbers together and divide by 3, we should get 749.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 749 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 749 * 3 = x + y + z
- So, the sum of our three numbers should be: 2247
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2247.
Solution 1:
749, 749, 749
Verification:
(749 + 749 + 749) / 3 = 2247 / 3 ≈ 749
This solution is correct!
Solution 2:
749, 749, 749
Verification:
(749 + 749 + 749) / 3 = 2247 / 3 ≈ 749
This solution is correct!
Solution 3:
490, 1174, 583
Verification:
(490 + 1174 + 583) / 3 = 2247 / 3 ≈ 749
This solution is correct!
Solution 4:
1974, 180, 93
Verification:
(1974 + 180 + 93) / 3 = 2247 / 3 ≈ 749
This solution is correct!
Solution 5:
53, 424, 1770
Verification:
(53 + 424 + 1770) / 3 = 2247 / 3 ≈ 749
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 2247 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.