A hardware store buys outdoor lights for $\$ 7.00$ per dozen less $20 \%, 19 \%$. The store's overhead is $48 \%$ of cost and the required profit is $25 \%$ of cost. For how much per dozen should the lights be sold? The selling price should be $\$ 783$ per dozen. (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：First, calculate the cost price per dozen after the discounts: \(\$7.00 \times (1 - 0.20) \times (1 - 0.19) = \$7.00 \times 0.80 \times 0.81 = \$4.536\)

Step 2 ：Next, calculate the overhead cost: \(0.48 \times \$4.536 = \$2.17728\)

Step 3 ：Now, calculate the required profit: \(0.25 \times \$4.536 = \$1.134\)

Step 4 ：Add the cost price, overhead cost, and required profit to find the selling price per dozen: \(\$4.536 + \$2.17728 + \$1.134 = \$7.84728\)

Step 5 ：Round the selling price to the nearest cent: \(\boxed{\$7.85}\)