Grayson is working two summer jobs, making $6 per hour walking dogs and making $10 per hour clearing tables. In a given week, he can work at most 18 total hours and must earn no less than $140. If Grayson worked 13 hours clearing tables, determine the minimum number of whole hours walking dogs that he must work to meet his requirements.

Let's denote the number of hours Grayson works walking dogs as x . He has a total of 18 hours available, and if he has already worked 13 hours clearing tables, the remaining time for walking dogs is 18 - 13 = 5 hours.

Now, let's calculate the minimum amount he can earn. From walking dogs, he makes $6 per hour, so the earnings from walking dogs would be 6x dollars. From clearing tables, he makes $10 per hour, and since he worked 13 hours, the earnings from clearing tables would be 10 * 13 dollars.

The total earnings must be at least $140, so we can write the inequality:

6x + (10 * 13) >= 140

Now, you can solve for x to find the minimum number of whole hours Grayson must work walking dogs.