What three numbers have an average of 196?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 196. This means if we add these three numbers together and divide by 3, we should get 196.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 196 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 196 * 3 = x + y + z
- So, the sum of our three numbers should be: 588
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 588.
Solution 1:
196, 196, 196
Verification:
(196 + 196 + 196) / 3 = 588 / 3 ≈ 196
This solution is correct!
Solution 2:
196, 196, 196
Verification:
(196 + 196 + 196) / 3 = 588 / 3 ≈ 196
This solution is correct!
Solution 3:
196, 364, 28
Verification:
(196 + 364 + 28) / 3 = 588 / 3 ≈ 196
This solution is correct!
Solution 4:
451, 98, 39
Verification:
(451 + 98 + 39) / 3 = 588 / 3 ≈ 196
This solution is correct!
Solution 5:
416, 87, 85
Verification:
(416 + 87 + 85) / 3 = 588 / 3 ≈ 196
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 588 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.