What three numbers have an average of 654?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 654. This means if we add these three numbers together and divide by 3, we should get 654.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 654 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 654 * 3 = x + y + z
- So, the sum of our three numbers should be: 1962
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1962.
Solution 1:
654, 654, 654
Verification:
(654 + 654 + 654) / 3 = 1962 / 3 ≈ 654
This solution is correct!
Solution 2:
654, 654, 654
Verification:
(654 + 654 + 654) / 3 = 1962 / 3 ≈ 654
This solution is correct!
Solution 3:
1379, 214, 369
Verification:
(1379 + 214 + 369) / 3 = 1962 / 3 ≈ 654
This solution is correct!
Solution 4:
254, 901, 807
Verification:
(254 + 901 + 807) / 3 = 1962 / 3 ≈ 654
This solution is correct!
Solution 5:
1513, 201, 248
Verification:
(1513 + 201 + 248) / 3 = 1962 / 3 ≈ 654
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 1962 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.