What three numbers have an average of 157?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 157. This means if we add these three numbers together and divide by 3, we should get 157.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 157 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 157 * 3 = x + y + z
- So, the sum of our three numbers should be: 471
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 471.
Solution 1:
157, 157, 157
Verification:
(157 + 157 + 157) / 3 = 471 / 3 ≈ 157
This solution is correct!
Solution 2:
157, 157, 157
Verification:
(157 + 157 + 157) / 3 = 471 / 3 ≈ 157
This solution is correct!
Solution 3:
465, 1, 5
Verification:
(465 + 1 + 5) / 3 = 471 / 3 ≈ 157
This solution is correct!
Solution 4:
246, 17, 208
Verification:
(246 + 17 + 208) / 3 = 471 / 3 ≈ 157
This solution is correct!
Solution 5:
81, 359, 31
Verification:
(81 + 359 + 31) / 3 = 471 / 3 ≈ 157
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 471 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.