What three numbers have an average of 211?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 211. This means if we add these three numbers together and divide by 3, we should get 211.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 211 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 211 * 3 = x + y + z
- So, the sum of our three numbers should be: 633
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 633.
Solution 1:
211, 211, 211
Verification:
(211 + 211 + 211) / 3 = 633 / 3 ≈ 211
This solution is correct!
Solution 2:
211, 211, 211
Verification:
(211 + 211 + 211) / 3 = 633 / 3 ≈ 211
This solution is correct!
Solution 3:
237, 107, 289
Verification:
(237 + 107 + 289) / 3 = 633 / 3 ≈ 211
This solution is correct!
Solution 4:
464, 20, 149
Verification:
(464 + 20 + 149) / 3 = 633 / 3 ≈ 211
This solution is correct!
Solution 5:
73, 443, 117
Verification:
(73 + 443 + 117) / 3 = 633 / 3 ≈ 211
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 633 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.