What three numbers have an average of 220?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 220. This means if we add these three numbers together and divide by 3, we should get 220.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 220 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 220 * 3 = x + y + z
- So, the sum of our three numbers should be: 660
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 660.
Solution 1:
220, 220, 220
Verification:
(220 + 220 + 220) / 3 = 660 / 3 ≈ 220
This solution is correct!
Solution 2:
220, 220, 220
Verification:
(220 + 220 + 220) / 3 = 660 / 3 ≈ 220
This solution is correct!
Solution 3:
429, 205, 26
Verification:
(429 + 205 + 26) / 3 = 660 / 3 ≈ 220
This solution is correct!
Solution 4:
240, 416, 4
Verification:
(240 + 416 + 4) / 3 = 660 / 3 ≈ 220
This solution is correct!
Solution 5:
212, 274, 174
Verification:
(212 + 274 + 174) / 3 = 660 / 3 ≈ 220
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 660 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.