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:
1979, 358, 564
Verification:
(1979 + 358 + 564) / 3 = 2901 / 3 ≈ 967
This solution is correct!
Solution 4:
2042, 648, 211
Verification:
(2042 + 648 + 211) / 3 = 2901 / 3 ≈ 967
This solution is correct!
Solution 5:
170, 2135, 596
Verification:
(170 + 2135 + 596) / 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.