What three numbers have an average of 541?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 541. This means if we add these three numbers together and divide by 3, we should get 541.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 541 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 541 * 3 = x + y + z
- So, the sum of our three numbers should be: 1623
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1623.
Solution 1:
541, 541, 541
Verification:
(541 + 541 + 541) / 3 = 1623 / 3 ≈ 541
This solution is correct!
Solution 2:
541, 541, 541
Verification:
(541 + 541 + 541) / 3 = 1623 / 3 ≈ 541
This solution is correct!
Solution 3:
1215, 285, 123
Verification:
(1215 + 285 + 123) / 3 = 1623 / 3 ≈ 541
This solution is correct!
Solution 4:
700, 34, 889
Verification:
(700 + 34 + 889) / 3 = 1623 / 3 ≈ 541
This solution is correct!
Solution 5:
85, 844, 694
Verification:
(85 + 844 + 694) / 3 = 1623 / 3 ≈ 541
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 1623 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.