What three numbers have an average of 190?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 190. This means if we add these three numbers together and divide by 3, we should get 190.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 190 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 190 * 3 = x + y + z
- So, the sum of our three numbers should be: 570
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 570.
Solution 1:
190, 190, 190
Verification:
(190 + 190 + 190) / 3 = 570 / 3 ≈ 190
This solution is correct!
Solution 2:
190, 190, 190
Verification:
(190 + 190 + 190) / 3 = 570 / 3 ≈ 190
This solution is correct!
Solution 3:
206, 79, 285
Verification:
(206 + 79 + 285) / 3 = 570 / 3 ≈ 190
This solution is correct!
Solution 4:
182, 33, 355
Verification:
(182 + 33 + 355) / 3 = 570 / 3 ≈ 190
This solution is correct!
Solution 5:
454, 33, 83
Verification:
(454 + 33 + 83) / 3 = 570 / 3 ≈ 190
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 570 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.