What three numbers have an average of 986?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 986. This means if we add these three numbers together and divide by 3, we should get 986.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 986 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 986 * 3 = x + y + z
- So, the sum of our three numbers should be: 2958
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2958.
Solution 1:
986, 986, 986
Verification:
(986 + 986 + 986) / 3 = 2958 / 3 ≈ 986
This solution is correct!
Solution 2:
986, 986, 986
Verification:
(986 + 986 + 986) / 3 = 2958 / 3 ≈ 986
This solution is correct!
Solution 3:
2094, 848, 16
Verification:
(2094 + 848 + 16) / 3 = 2958 / 3 ≈ 986
This solution is correct!
Solution 4:
1779, 390, 789
Verification:
(1779 + 390 + 789) / 3 = 2958 / 3 ≈ 986
This solution is correct!
Solution 5:
680, 2093, 185
Verification:
(680 + 2093 + 185) / 3 = 2958 / 3 ≈ 986
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 2958 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.