What three numbers have an average of 901?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 901. This means if we add these three numbers together and divide by 3, we should get 901.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 901 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 901 * 3 = x + y + z
- So, the sum of our three numbers should be: 2703
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2703.
Solution 1:
901, 901, 901
Verification:
(901 + 901 + 901) / 3 = 2703 / 3 ≈ 901
This solution is correct!
Solution 2:
901, 901, 901
Verification:
(901 + 901 + 901) / 3 = 2703 / 3 ≈ 901
This solution is correct!
Solution 3:
320, 144, 2239
Verification:
(320 + 144 + 2239) / 3 = 2703 / 3 ≈ 901
This solution is correct!
Solution 4:
1721, 683, 299
Verification:
(1721 + 683 + 299) / 3 = 2703 / 3 ≈ 901
This solution is correct!
Solution 5:
1506, 223, 974
Verification:
(1506 + 223 + 974) / 3 = 2703 / 3 ≈ 901
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 2703 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.