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.