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:
57, 35, 514
Verification:
(57 + 35 + 514) / 3 = 606 / 3 ≈ 202
This solution is correct!
Solution 4:
159, 80, 367
Verification:
(159 + 80 + 367) / 3 = 606 / 3 ≈ 202
This solution is correct!
Solution 5:
93, 155, 358
Verification:
(93 + 155 + 358) / 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.