If it's an EOT you just know they aren't particularly looking for a good job to be done and are therefore always going to look for the cheapest.
These can be harder sales as you don't know how much the other carpet cleaners are going to charge but there
are ways of winning them over....
.
I know a C/C who used to say that whatever price they get quoted from a competitor, they will charge £5 less than the cheapest quote they get... Obviously you are relying on them telling the competition of your offer. Therefore, (theoretically) they throw in a really silly quote to see you off...
Then when they ring back and say "The other guy has come down to £50 for a 3 bed whole house carpet clean!"
This fella would say when the prospect tried to book him in "I'm afraid you're going to have to go with them, I'm booked up that week....!"