What three numbers have an average of 458?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 458. This means if we add these three numbers together and divide by 3, we should get 458.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 458 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 458 * 3 = x + y + z
- So, the sum of our three numbers should be: 1374
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1374.
Solution 1:
458, 458, 458
Verification:
(458 + 458 + 458) / 3 = 1374 / 3 ≈ 458
This solution is correct!
Solution 2:
458, 458, 458
Verification:
(458 + 458 + 458) / 3 = 1374 / 3 ≈ 458
This solution is correct!
Solution 3:
1090, 51, 233
Verification:
(1090 + 51 + 233) / 3 = 1374 / 3 ≈ 458
This solution is correct!
Solution 4:
890, 309, 175
Verification:
(890 + 309 + 175) / 3 = 1374 / 3 ≈ 458
This solution is correct!
Solution 5:
1286, 53, 35
Verification:
(1286 + 53 + 35) / 3 = 1374 / 3 ≈ 458
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 1374 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.