What three numbers have an average of 189?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 189. This means if we add these three numbers together and divide by 3, we should get 189.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 189 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 189 * 3 = x + y + z
- So, the sum of our three numbers should be: 567
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 567.
Solution 1:
189, 189, 189
Verification:
(189 + 189 + 189) / 3 = 567 / 3 ≈ 189
This solution is correct!
Solution 2:
189, 189, 189
Verification:
(189 + 189 + 189) / 3 = 567 / 3 ≈ 189
This solution is correct!
Solution 3:
385, 108, 74
Verification:
(385 + 108 + 74) / 3 = 567 / 3 ≈ 189
This solution is correct!
Solution 4:
104, 250, 213
Verification:
(104 + 250 + 213) / 3 = 567 / 3 ≈ 189
This solution is correct!
Solution 5:
152, 299, 116
Verification:
(152 + 299 + 116) / 3 = 567 / 3 ≈ 189
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 567 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.