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:
352, 76, 40
Verification:
(352 + 76 + 40) / 3 = 468 / 3 ≈ 156
This solution is correct!
Solution 4:
406, 37, 25
Verification:
(406 + 37 + 25) / 3 = 468 / 3 ≈ 156
This solution is correct!
Solution 5:
117, 219, 132
Verification:
(117 + 219 + 132) / 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.