What three numbers have an average of 431?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 431. This means if we add these three numbers together and divide by 3, we should get 431.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 431 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 431 * 3 = x + y + z
- So, the sum of our three numbers should be: 1293
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1293.
Solution 1:
431, 431, 431
Verification:
(431 + 431 + 431) / 3 = 1293 / 3 ≈ 431
This solution is correct!
Solution 2:
431, 431, 431
Verification:
(431 + 431 + 431) / 3 = 1293 / 3 ≈ 431
This solution is correct!
Solution 3:
1109, 37, 147
Verification:
(1109 + 37 + 147) / 3 = 1293 / 3 ≈ 431
This solution is correct!
Solution 4:
983, 256, 54
Verification:
(983 + 256 + 54) / 3 = 1293 / 3 ≈ 431
This solution is correct!
Solution 5:
1100, 51, 142
Verification:
(1100 + 51 + 142) / 3 = 1293 / 3 ≈ 431
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 1293 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.