Sandy's Trap Real Estate specializes in properties for sale around a new golf community development on the coast. Sandy's receives $820$ leads each month from a golfing magazine ad that targets retirees. The leads are divided equally among the $7$ realtors who then follow$-$up with a phone call to determine the potential client's interest and ability to purchase. After the phone call, qualified prospects are offered a free round of golf if they will attend a sales presentation. A percentage of the people who agree to the sales presentation then decide to take one or more tours of homes available for sale in the golf community. On average, clients who reach this stage of the purchase process take $3$ tours.

Sandy, the owner, had calcualted that the average time for a salesperson to call a warm lead was $30$ minutes, the average sales presentation lasts $30$ minutes, each tour normally takes $5$ hours, and the closing $($the actual purchase$)$ averages $2$ hours. Sandy had also collected the following data for a year's worth of leads for the company, and his leading salesperson, Palma:

Salesperson $\%$ Leads$-->$Sales Presentation $\%$ Sales Presentation$-->$Tour $\%$ Tour$-->$Purchase

Company $10\%38\%20\%$

Palma $21\%18\%25\%$

Finally, the average home price was $$265,000$ and the total commission rate was set at $6\%$ of the sales price of the home which is split between the realtor and the company. Therefore, the salesperson receives $3\%$ and Sandy receives $3\%$ to cover overhead and expenses.

Based on the data provided, how many homes did Palma sell?