What three numbers have an average of 991?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 991. This means if we add these three numbers together and divide by 3, we should get 991.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 991 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 991 * 3 = x + y + z
- So, the sum of our three numbers should be: 2973
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2973.
Solution 1:
991, 991, 991
Verification:
(991 + 991 + 991) / 3 = 2973 / 3 ≈ 991
This solution is correct!
Solution 2:
991, 991, 991
Verification:
(991 + 991 + 991) / 3 = 2973 / 3 ≈ 991
This solution is correct!
Solution 3:
1304, 123, 1546
Verification:
(1304 + 123 + 1546) / 3 = 2973 / 3 ≈ 991
This solution is correct!
Solution 4:
570, 422, 1981
Verification:
(570 + 422 + 1981) / 3 = 2973 / 3 ≈ 991
This solution is correct!
Solution 5:
714, 1314, 945
Verification:
(714 + 1314 + 945) / 3 = 2973 / 3 ≈ 991
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 2973 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.