What three numbers have an average of 303?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 303. This means if we add these three numbers together and divide by 3, we should get 303.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 303 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 303 * 3 = x + y + z
- So, the sum of our three numbers should be: 909
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 909.
Solution 1:
303, 303, 303
Verification:
(303 + 303 + 303) / 3 = 909 / 3 ≈ 303
This solution is correct!
Solution 2:
303, 303, 303
Verification:
(303 + 303 + 303) / 3 = 909 / 3 ≈ 303
This solution is correct!
Solution 3:
19, 696, 194
Verification:
(19 + 696 + 194) / 3 = 909 / 3 ≈ 303
This solution is correct!
Solution 4:
167, 602, 140
Verification:
(167 + 602 + 140) / 3 = 909 / 3 ≈ 303
This solution is correct!
Solution 5:
457, 433, 19
Verification:
(457 + 433 + 19) / 3 = 909 / 3 ≈ 303
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 909 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.