What three numbers have an average of 159?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 159. This means if we add these three numbers together and divide by 3, we should get 159.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 159 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 159 * 3 = x + y + z
- So, the sum of our three numbers should be: 477
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 477.
Solution 1:
159, 159, 159
Verification:
(159 + 159 + 159) / 3 = 477 / 3 ≈ 159
This solution is correct!
Solution 2:
159, 159, 159
Verification:
(159 + 159 + 159) / 3 = 477 / 3 ≈ 159
This solution is correct!
Solution 3:
218, 62, 197
Verification:
(218 + 62 + 197) / 3 = 477 / 3 ≈ 159
This solution is correct!
Solution 4:
12, 198, 267
Verification:
(12 + 198 + 267) / 3 = 477 / 3 ≈ 159
This solution is correct!
Solution 5:
406, 31, 40
Verification:
(406 + 31 + 40) / 3 = 477 / 3 ≈ 159
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 477 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.