What three numbers have an average of 742?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 742. This means if we add these three numbers together and divide by 3, we should get 742.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 742 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 742 * 3 = x + y + z
- So, the sum of our three numbers should be: 2226
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2226.
Solution 1:
742, 742, 742
Verification:
(742 + 742 + 742) / 3 = 2226 / 3 ≈ 742
This solution is correct!
Solution 2:
742, 742, 742
Verification:
(742 + 742 + 742) / 3 = 2226 / 3 ≈ 742
This solution is correct!
Solution 3:
139, 52, 2035
Verification:
(139 + 52 + 2035) / 3 = 2226 / 3 ≈ 742
This solution is correct!
Solution 4:
868, 1046, 312
Verification:
(868 + 1046 + 312) / 3 = 2226 / 3 ≈ 742
This solution is correct!
Solution 5:
790, 801, 635
Verification:
(790 + 801 + 635) / 3 = 2226 / 3 ≈ 742
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 2226 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.