What three numbers have an average of 152?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 152. This means if we add these three numbers together and divide by 3, we should get 152.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 152 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 152 * 3 = x + y + z
- So, the sum of our three numbers should be: 456
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 456.
Solution 1:
152, 152, 152
Verification:
(152 + 152 + 152) / 3 = 456 / 3 ≈ 152
This solution is correct!
Solution 2:
152, 152, 152
Verification:
(152 + 152 + 152) / 3 = 456 / 3 ≈ 152
This solution is correct!
Solution 3:
421, 34, 1
Verification:
(421 + 34 + 1) / 3 = 456 / 3 ≈ 152
This solution is correct!
Solution 4:
199, 51, 206
Verification:
(199 + 51 + 206) / 3 = 456 / 3 ≈ 152
This solution is correct!
Solution 5:
6, 82, 368
Verification:
(6 + 82 + 368) / 3 = 456 / 3 ≈ 152
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 456 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.