What three numbers have an average of 221?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 221. This means if we add these three numbers together and divide by 3, we should get 221.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 221 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 221 * 3 = x + y + z
- So, the sum of our three numbers should be: 663
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 663.
Solution 1:
221, 221, 221
Verification:
(221 + 221 + 221) / 3 = 663 / 3 ≈ 221
This solution is correct!
Solution 2:
221, 221, 221
Verification:
(221 + 221 + 221) / 3 = 663 / 3 ≈ 221
This solution is correct!
Solution 3:
180, 328, 155
Verification:
(180 + 328 + 155) / 3 = 663 / 3 ≈ 221
This solution is correct!
Solution 4:
417, 64, 182
Verification:
(417 + 64 + 182) / 3 = 663 / 3 ≈ 221
This solution is correct!
Solution 5:
105, 70, 488
Verification:
(105 + 70 + 488) / 3 = 663 / 3 ≈ 221
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 663 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.