What three numbers have an average of 807?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 807. This means if we add these three numbers together and divide by 3, we should get 807.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 807 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 807 * 3 = x + y + z
- So, the sum of our three numbers should be: 2421
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2421.
Solution 1:
807, 807, 807
Verification:
(807 + 807 + 807) / 3 = 2421 / 3 ≈ 807
This solution is correct!
Solution 2:
807, 807, 807
Verification:
(807 + 807 + 807) / 3 = 2421 / 3 ≈ 807
This solution is correct!
Solution 3:
446, 1956, 19
Verification:
(446 + 1956 + 19) / 3 = 2421 / 3 ≈ 807
This solution is correct!
Solution 4:
989, 147, 1285
Verification:
(989 + 147 + 1285) / 3 = 2421 / 3 ≈ 807
This solution is correct!
Solution 5:
675, 235, 1511
Verification:
(675 + 235 + 1511) / 3 = 2421 / 3 ≈ 807
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 2421 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.