What three numbers have an average of 462?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 462. This means if we add these three numbers together and divide by 3, we should get 462.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 462 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 462 * 3 = x + y + z
- So, the sum of our three numbers should be: 1386
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1386.
Solution 1:
462, 462, 462
Verification:
(462 + 462 + 462) / 3 = 1386 / 3 ≈ 462
This solution is correct!
Solution 2:
462, 462, 462
Verification:
(462 + 462 + 462) / 3 = 1386 / 3 ≈ 462
This solution is correct!
Solution 3:
1089, 277, 20
Verification:
(1089 + 277 + 20) / 3 = 1386 / 3 ≈ 462
This solution is correct!
Solution 4:
540, 740, 106
Verification:
(540 + 740 + 106) / 3 = 1386 / 3 ≈ 462
This solution is correct!
Solution 5:
167, 105, 1114
Verification:
(167 + 105 + 1114) / 3 = 1386 / 3 ≈ 462
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 1386 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.