What three numbers have an average of 962?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 962. This means if we add these three numbers together and divide by 3, we should get 962.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 962 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 962 * 3 = x + y + z
- So, the sum of our three numbers should be: 2886
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2886.
Solution 1:
962, 962, 962
Verification:
(962 + 962 + 962) / 3 = 2886 / 3 ≈ 962
This solution is correct!
Solution 2:
962, 962, 962
Verification:
(962 + 962 + 962) / 3 = 2886 / 3 ≈ 962
This solution is correct!
Solution 3:
153, 2405, 328
Verification:
(153 + 2405 + 328) / 3 = 2886 / 3 ≈ 962
This solution is correct!
Solution 4:
2780, 105, 1
Verification:
(2780 + 105 + 1) / 3 = 2886 / 3 ≈ 962
This solution is correct!
Solution 5:
1130, 172, 1584
Verification:
(1130 + 172 + 1584) / 3 = 2886 / 3 ≈ 962
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 2886 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.