What three numbers have an average of 832?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 832. This means if we add these three numbers together and divide by 3, we should get 832.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 832 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 832 * 3 = x + y + z
- So, the sum of our three numbers should be: 2496
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2496.
Solution 1:
832, 832, 832
Verification:
(832 + 832 + 832) / 3 = 2496 / 3 ≈ 832
This solution is correct!
Solution 2:
832, 832, 832
Verification:
(832 + 832 + 832) / 3 = 2496 / 3 ≈ 832
This solution is correct!
Solution 3:
433, 1930, 133
Verification:
(433 + 1930 + 133) / 3 = 2496 / 3 ≈ 832
This solution is correct!
Solution 4:
124, 1196, 1176
Verification:
(124 + 1196 + 1176) / 3 = 2496 / 3 ≈ 832
This solution is correct!
Solution 5:
164, 35, 2297
Verification:
(164 + 35 + 2297) / 3 = 2496 / 3 ≈ 832
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 2496 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.