Calculations from checkboxes

I am creating a form in which I will be counting the number of checkboxes that are checked in order to do some calculations.  Here's what I'm doing.

The item will display a number of classes for a user to select.  Those classes selected will be passed on in the email.  Based on the number of classes checked, I can count those to do my calculations.  The first class will cost $20 and every one after that will be $10. So my questions are...

1. Where would I place the PHP code in my form to do the calculations?
2. Is my code for calculating correct? (I am assuming I use the name field and not the field key)
   $howMany = sizeof ( $_REQUEST[ 'classes' ] ); //count the number of checkboxes checked
$total = 20 + (($howMany - 1) * 10)); //total fees
3. How and where do I assign the "$total" variable to a hidden form element i.e. [amount] to be sent in the email? Can I still use PHP and add this to the code above?
   $_POST['amount'] = $total;
   This way I can use "[amount]" when crafting my message and for sending the amount to Paypal.

Thanks for your help.