What three numbers have an average of 601?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 601. This means if we add these three numbers together and divide by 3, we should get 601.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 601 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 601 * 3 = x + y + z
- So, the sum of our three numbers should be: 1803
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1803.
Solution 1:
601, 601, 601
Verification:
(601 + 601 + 601) / 3 = 1803 / 3 ≈ 601
This solution is correct!
Solution 2:
601, 601, 601
Verification:
(601 + 601 + 601) / 3 = 1803 / 3 ≈ 601
This solution is correct!
Solution 3:
131, 1437, 235
Verification:
(131 + 1437 + 235) / 3 = 1803 / 3 ≈ 601
This solution is correct!
Solution 4:
50, 369, 1384
Verification:
(50 + 369 + 1384) / 3 = 1803 / 3 ≈ 601
This solution is correct!
Solution 5:
1594, 164, 45
Verification:
(1594 + 164 + 45) / 3 = 1803 / 3 ≈ 601
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 1803 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.