What three numbers have an average of 155?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 155. This means if we add these three numbers together and divide by 3, we should get 155.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 155 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 155 * 3 = x + y + z
- So, the sum of our three numbers should be: 465
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 465.
Solution 1:
155, 155, 155
Verification:
(155 + 155 + 155) / 3 = 465 / 3 ≈ 155
This solution is correct!
Solution 2:
155, 155, 155
Verification:
(155 + 155 + 155) / 3 = 465 / 3 ≈ 155
This solution is correct!
Solution 3:
33, 311, 121
Verification:
(33 + 311 + 121) / 3 = 465 / 3 ≈ 155
This solution is correct!
Solution 4:
285, 145, 35
Verification:
(285 + 145 + 35) / 3 = 465 / 3 ≈ 155
This solution is correct!
Solution 5:
327, 18, 120
Verification:
(327 + 18 + 120) / 3 = 465 / 3 ≈ 155
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 465 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.