### Instruction: A palindrome is an integer that reads the same forward and backward, such as 3663. What percent of the palindromes between 100 and 500 contain at least one 5?### Response: I need to find the total number of palindromes between 100 and 500, and then the number of those that contain at least one 5.
To be a palindrome, the first and last digits must be the same, and the middle digit can be anything.
So, for the first digit, I have four choices: 1, 2, 3, or 4.
For the middle digit, I have 10 choices: 0, 1, 2, ..., 9.
For the last digit, I have no choice: it must be the same as the first digit.
Therefore, the total number of palindromes between 100 and 500 is 4 times 10, or 40.
Now, how many of them contain at least one 5?
Well, the only way to have a 5 is to have it as the middle digit, since the first and last digits must be 1, 2, 3, or 4.
So, for the middle digit, I have only one choice: 5.
For the first and last digits, I still have four choices: 1, 2, 3, or 4.
Therefore, the number of palindromes between 100 and 500 that contain at least one 5 is 4 times 1, or 4.
To find the percent, I need to divide the number of palindromes with at least one 5 by the total number of palindromes, and multiply by 100.
So, the percent is (4/40) times 100, which simplifies to 10.
Therefore, 10% of the palindromes between 100 and 500 contain at least one 5.