What three numbers have an average of 423?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 423. This means if we add these three numbers together and divide by 3, we should get 423.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 423 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 423 * 3 = x + y + z
- So, the sum of our three numbers should be: 1269
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1269.
Solution 1:
423, 423, 423
Verification:
(423 + 423 + 423) / 3 = 1269 / 3 ≈ 423
This solution is correct!
Solution 2:
423, 423, 423
Verification:
(423 + 423 + 423) / 3 = 1269 / 3 ≈ 423
This solution is correct!
Solution 3:
686, 243, 340
Verification:
(686 + 243 + 340) / 3 = 1269 / 3 ≈ 423
This solution is correct!
Solution 4:
302, 894, 73
Verification:
(302 + 894 + 73) / 3 = 1269 / 3 ≈ 423
This solution is correct!
Solution 5:
1205, 32, 32
Verification:
(1205 + 32 + 32) / 3 = 1269 / 3 ≈ 423
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 1269 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.