What three numbers have an average of 253?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 253. This means if we add these three numbers together and divide by 3, we should get 253.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 253 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 253 * 3 = x + y + z
- So, the sum of our three numbers should be: 759
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 759.
Solution 1:
253, 253, 253
Verification:
(253 + 253 + 253) / 3 = 759 / 3 ≈ 253
This solution is correct!
Solution 2:
253, 253, 253
Verification:
(253 + 253 + 253) / 3 = 759 / 3 ≈ 253
This solution is correct!
Solution 3:
455, 297, 7
Verification:
(455 + 297 + 7) / 3 = 759 / 3 ≈ 253
This solution is correct!
Solution 4:
195, 402, 162
Verification:
(195 + 402 + 162) / 3 = 759 / 3 ≈ 253
This solution is correct!
Solution 5:
49, 208, 502
Verification:
(49 + 208 + 502) / 3 = 759 / 3 ≈ 253
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 759 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.