What three numbers have an average of 208?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 208. This means if we add these three numbers together and divide by 3, we should get 208.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 208 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 208 * 3 = x + y + z
- So, the sum of our three numbers should be: 624
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 624.
Solution 1:
208, 208, 208
Verification:
(208 + 208 + 208) / 3 = 624 / 3 ≈ 208
This solution is correct!
Solution 2:
208, 208, 208
Verification:
(208 + 208 + 208) / 3 = 624 / 3 ≈ 208
This solution is correct!
Solution 3:
588, 26, 10
Verification:
(588 + 26 + 10) / 3 = 624 / 3 ≈ 208
This solution is correct!
Solution 4:
53, 7, 564
Verification:
(53 + 7 + 564) / 3 = 624 / 3 ≈ 208
This solution is correct!
Solution 5:
194, 73, 357
Verification:
(194 + 73 + 357) / 3 = 624 / 3 ≈ 208
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 624 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.