What three numbers have an average of 967?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 967. This means if we add these three numbers together and divide by 3, we should get 967.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 967 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 967 * 3 = x + y + z
- So, the sum of our three numbers should be: 2901
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2901.
Solution 1:
967, 967, 967
Verification:
(967 + 967 + 967) / 3 = 2901 / 3 ≈ 967
This solution is correct!
Solution 2:
967, 967, 967
Verification:
(967 + 967 + 967) / 3 = 2901 / 3 ≈ 967
This solution is correct!
Solution 3:
2678, 137, 86
Verification:
(2678 + 137 + 86) / 3 = 2901 / 3 ≈ 967
This solution is correct!
Solution 4:
99, 2084, 718
Verification:
(99 + 2084 + 718) / 3 = 2901 / 3 ≈ 967
This solution is correct!
Solution 5:
1461, 820, 620
Verification:
(1461 + 820 + 620) / 3 = 2901 / 3 ≈ 967
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 2901 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.