Let's call H the number of hours she dances. So, one group of sponsors will donate a total, in dollars:

Also, the other group of sponsors will donate a total, in dollars:

So, she will make:

For that value to be at least $500, we have:

Now, we can find the number of hours Trace should dance if she wants to raise at least $500 by solving the above inequality.
We obtain:

Therefore, she should dance for at least 70.83 hours. Rounding to the nearest integer hour, we can say she should dance for at least 71 hours.