What three numbers have an average of 525?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 525. This means if we add these three numbers together and divide by 3, we should get 525.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 525 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 525 * 3 = x + y + z
- So, the sum of our three numbers should be: 1575
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1575.
Solution 1:
525, 525, 525
Verification:
(525 + 525 + 525) / 3 = 1575 / 3 ≈ 525
This solution is correct!
Solution 2:
525, 525, 525
Verification:
(525 + 525 + 525) / 3 = 1575 / 3 ≈ 525
This solution is correct!
Solution 3:
1133, 270, 172
Verification:
(1133 + 270 + 172) / 3 = 1575 / 3 ≈ 525
This solution is correct!
Solution 4:
110, 414, 1051
Verification:
(110 + 414 + 1051) / 3 = 1575 / 3 ≈ 525
This solution is correct!
Solution 5:
696, 123, 756
Verification:
(696 + 123 + 756) / 3 = 1575 / 3 ≈ 525
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 1575 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.