What three numbers have an average of 156?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 156. This means if we add these three numbers together and divide by 3, we should get 156.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 156 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 156 * 3 = x + y + z
- So, the sum of our three numbers should be: 468
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 468.
Solution 1:
156, 156, 156
Verification:
(156 + 156 + 156) / 3 = 468 / 3 ≈ 156
This solution is correct!
Solution 2:
156, 156, 156
Verification:
(156 + 156 + 156) / 3 = 468 / 3 ≈ 156
This solution is correct!
Solution 3:
345, 17, 106
Verification:
(345 + 17 + 106) / 3 = 468 / 3 ≈ 156
This solution is correct!
Solution 4:
34, 254, 180
Verification:
(34 + 254 + 180) / 3 = 468 / 3 ≈ 156
This solution is correct!
Solution 5:
136, 176, 156
Verification:
(136 + 176 + 156) / 3 = 468 / 3 ≈ 156
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 468 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.