What three numbers have an average of 130?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 130. This means if we add these three numbers together and divide by 3, we should get 130.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 130 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 130 * 3 = x + y + z
- So, the sum of our three numbers should be: 390
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 390.
Solution 1:
130, 130, 130
Verification:
(130 + 130 + 130) / 3 = 390 / 3 ≈ 130
This solution is correct!
Solution 2:
130, 130, 130
Verification:
(130 + 130 + 130) / 3 = 390 / 3 ≈ 130
This solution is correct!
Solution 3:
16, 181, 193
Verification:
(16 + 181 + 193) / 3 = 390 / 3 ≈ 130
This solution is correct!
Solution 4:
340, 19, 31
Verification:
(340 + 19 + 31) / 3 = 390 / 3 ≈ 130
This solution is correct!
Solution 5:
162, 28, 200
Verification:
(162 + 28 + 200) / 3 = 390 / 3 ≈ 130
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 390 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.