What three numbers have an average of 542?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 542. This means if we add these three numbers together and divide by 3, we should get 542.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 542 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 542 * 3 = x + y + z
- So, the sum of our three numbers should be: 1626
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1626.
Solution 1:
542, 542, 542
Verification:
(542 + 542 + 542) / 3 = 1626 / 3 ≈ 542
This solution is correct!
Solution 2:
542, 542, 542
Verification:
(542 + 542 + 542) / 3 = 1626 / 3 ≈ 542
This solution is correct!
Solution 3:
699, 825, 102
Verification:
(699 + 825 + 102) / 3 = 1626 / 3 ≈ 542
This solution is correct!
Solution 4:
946, 437, 243
Verification:
(946 + 437 + 243) / 3 = 1626 / 3 ≈ 542
This solution is correct!
Solution 5:
932, 413, 281
Verification:
(932 + 413 + 281) / 3 = 1626 / 3 ≈ 542
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 1626 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.