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