What three numbers have an average of 987?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 987. This means if we add these three numbers together and divide by 3, we should get 987.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 987 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 987 * 3 = x + y + z
- So, the sum of our three numbers should be: 2961
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2961.
Solution 1:
987, 987, 987
Verification:
(987 + 987 + 987) / 3 = 2961 / 3 ≈ 987
This solution is correct!
Solution 2:
987, 987, 987
Verification:
(987 + 987 + 987) / 3 = 2961 / 3 ≈ 987
This solution is correct!
Solution 3:
1112, 441, 1408
Verification:
(1112 + 441 + 1408) / 3 = 2961 / 3 ≈ 987
This solution is correct!
Solution 4:
541, 1838, 582
Verification:
(541 + 1838 + 582) / 3 = 2961 / 3 ≈ 987
This solution is correct!
Solution 5:
2617, 148, 196
Verification:
(2617 + 148 + 196) / 3 = 2961 / 3 ≈ 987
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 2961 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.