What three numbers have an average of 985?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 985. This means if we add these three numbers together and divide by 3, we should get 985.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 985 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 985 * 3 = x + y + z
- So, the sum of our three numbers should be: 2955
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2955.
Solution 1:
985, 985, 985
Verification:
(985 + 985 + 985) / 3 = 2955 / 3 ≈ 985
This solution is correct!
Solution 2:
985, 985, 985
Verification:
(985 + 985 + 985) / 3 = 2955 / 3 ≈ 985
This solution is correct!
Solution 3:
93, 228, 2634
Verification:
(93 + 228 + 2634) / 3 = 2955 / 3 ≈ 985
This solution is correct!
Solution 4:
533, 543, 1879
Verification:
(533 + 543 + 1879) / 3 = 2955 / 3 ≈ 985
This solution is correct!
Solution 5:
1177, 891, 887
Verification:
(1177 + 891 + 887) / 3 = 2955 / 3 ≈ 985
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 2955 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.