What three numbers have an average of 662?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 662. This means if we add these three numbers together and divide by 3, we should get 662.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 662 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 662 * 3 = x + y + z
- So, the sum of our three numbers should be: 1986
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1986.
Solution 1:
662, 662, 662
Verification:
(662 + 662 + 662) / 3 = 1986 / 3 ≈ 662
This solution is correct!
Solution 2:
662, 662, 662
Verification:
(662 + 662 + 662) / 3 = 1986 / 3 ≈ 662
This solution is correct!
Solution 3:
326, 1253, 407
Verification:
(326 + 1253 + 407) / 3 = 1986 / 3 ≈ 662
This solution is correct!
Solution 4:
428, 1063, 495
Verification:
(428 + 1063 + 495) / 3 = 1986 / 3 ≈ 662
This solution is correct!
Solution 5:
779, 1087, 120
Verification:
(779 + 1087 + 120) / 3 = 1986 / 3 ≈ 662
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 1986 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.