What three numbers have an average of 302?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 302. This means if we add these three numbers together and divide by 3, we should get 302.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 302 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 302 * 3 = x + y + z
- So, the sum of our three numbers should be: 906
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 906.
Solution 1:
302, 302, 302
Verification:
(302 + 302 + 302) / 3 = 906 / 3 ≈ 302
This solution is correct!
Solution 2:
302, 302, 302
Verification:
(302 + 302 + 302) / 3 = 906 / 3 ≈ 302
This solution is correct!
Solution 3:
367, 318, 221
Verification:
(367 + 318 + 221) / 3 = 906 / 3 ≈ 302
This solution is correct!
Solution 4:
12, 448, 446
Verification:
(12 + 448 + 446) / 3 = 906 / 3 ≈ 302
This solution is correct!
Solution 5:
31, 854, 21
Verification:
(31 + 854 + 21) / 3 = 906 / 3 ≈ 302
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 906 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.