What three numbers have an average of 182?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 182. This means if we add these three numbers together and divide by 3, we should get 182.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 182 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 182 * 3 = x + y + z
- So, the sum of our three numbers should be: 546
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 546.
Solution 1:
182, 182, 182
Verification:
(182 + 182 + 182) / 3 = 546 / 3 ≈ 182
This solution is correct!
Solution 2:
182, 182, 182
Verification:
(182 + 182 + 182) / 3 = 546 / 3 ≈ 182
This solution is correct!
Solution 3:
70, 393, 83
Verification:
(70 + 393 + 83) / 3 = 546 / 3 ≈ 182
This solution is correct!
Solution 4:
350, 52, 144
Verification:
(350 + 52 + 144) / 3 = 546 / 3 ≈ 182
This solution is correct!
Solution 5:
491, 8, 47
Verification:
(491 + 8 + 47) / 3 = 546 / 3 ≈ 182
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 546 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.