What three numbers have an average of 202?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 202. This means if we add these three numbers together and divide by 3, we should get 202.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 202 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 202 * 3 = x + y + z
- So, the sum of our three numbers should be: 606
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 606.
Solution 1:
202, 202, 202
Verification:
(202 + 202 + 202) / 3 = 606 / 3 ≈ 202
This solution is correct!
Solution 2:
202, 202, 202
Verification:
(202 + 202 + 202) / 3 = 606 / 3 ≈ 202
This solution is correct!
Solution 3:
499, 38, 69
Verification:
(499 + 38 + 69) / 3 = 606 / 3 ≈ 202
This solution is correct!
Solution 4:
211, 200, 195
Verification:
(211 + 200 + 195) / 3 = 606 / 3 ≈ 202
This solution is correct!
Solution 5:
382, 203, 21
Verification:
(382 + 203 + 21) / 3 = 606 / 3 ≈ 202
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 606 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.