What three numbers have an average of 153?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 153. This means if we add these three numbers together and divide by 3, we should get 153.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 153 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 153 * 3 = x + y + z
- So, the sum of our three numbers should be: 459
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 459.
Solution 1:
153, 153, 153
Verification:
(153 + 153 + 153) / 3 = 459 / 3 ≈ 153
This solution is correct!
Solution 2:
153, 153, 153
Verification:
(153 + 153 + 153) / 3 = 459 / 3 ≈ 153
This solution is correct!
Solution 3:
359, 31, 69
Verification:
(359 + 31 + 69) / 3 = 459 / 3 ≈ 153
This solution is correct!
Solution 4:
99, 18, 342
Verification:
(99 + 18 + 342) / 3 = 459 / 3 ≈ 153
This solution is correct!
Solution 5:
247, 64, 148
Verification:
(247 + 64 + 148) / 3 = 459 / 3 ≈ 153
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 459 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.