What three numbers have an average of 998?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 998. This means if we add these three numbers together and divide by 3, we should get 998.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 998 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 998 * 3 = x + y + z
- So, the sum of our three numbers should be: 2994
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2994.
Solution 1:
998, 998, 998
Verification:
(998 + 998 + 998) / 3 = 2994 / 3 ≈ 998
This solution is correct!
Solution 2:
998, 998, 998
Verification:
(998 + 998 + 998) / 3 = 2994 / 3 ≈ 998
This solution is correct!
Solution 3:
1779, 59, 1156
Verification:
(1779 + 59 + 1156) / 3 = 2994 / 3 ≈ 998
This solution is correct!
Solution 4:
104, 2710, 180
Verification:
(104 + 2710 + 180) / 3 = 2994 / 3 ≈ 998
This solution is correct!
Solution 5:
840, 634, 1520
Verification:
(840 + 634 + 1520) / 3 = 2994 / 3 ≈ 998
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 2994 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.