And that is just wrong on your part for so many reasons. That is taking advantage of the situation. A good babysitter is worth their weight in gold.
Here, if you dont want to pay AT LEAST $10/hour for 1 child, you will not find a babysitter. I won't babysit for less than $12/hour for 1 child. I have 9 years of babysitting experience, a year of preschool/daycare experience plus infant/child CPR certification.
This will probably make me sound bad but when it comes to babysitting, I am worth more than $3/hour and I have the experience and 6 references to prove it.
Our babysitter is an in-home private babysitter. Our daughter is not the only child who goes to her. However, her rates are going to be high come September, especially for this area.
If your child is not the only one in her care, you need to add up what you each pay her for her hourly rate. Just because you aren't personally paying her $10/hour doesn't mean she isn't charging that much.
Also, as was mentioned by a PP, daily in-home care is often a bit less per hour, namely because 1)all the kids going are in effect subsidizing one another, 2) the income for the sitter is fairly regular, unlike booking someone for a random weekend evening, and 3) you often must pay the sitter whether or not your child goes that day.

I live around a fairly large city and yes there are those that pay $10+ an hr but there are quite a few that also take as low as $2 hr. I myself charge my best friend $2 hr to watch her almost 1 yr old for 11 hrs a day (I honestly would charge someone else $1-$3 more) I also watch a 1st and 4th grader afterschool the bus drops them off at my house and they are here from 3pm-8pm and I charge $8hr for that, mainly because of dinner, I take her son 1-2times a week to Taekwando, and the "night time" rate.