Blake finds that if he washes his car prior to going out on the town, more of his friends want to ride along with him. What theory would best explain his willingness to always wash and clean his car before going out?

the answer is: Thorndike's law of effect

According to Thorndike's law of effect, an individual will be more likely to do a certain action if that individual sure that he/she will get a satisfying result from doing that action.

In Blake's case, having more friends that willing to go out with him is the satisfying result that he seek. Since he realized that this tend to occur when he washed his car, he will become much more likely to repeat the action in the future,