The cost of shirts is $\$ 9.90$ each if 1,000 shirts are purchased. Harry sells 800 shirts before the football season begins at a $60 \%$ markup based on cost. What is the gross margin (markup) if Harry sells the remaining 200 shirts at a $30 \%$ reduction from the selling price?
The gross margin is $\$ \square$.
Answer
\(\boxed{\$4989.60}\) is the final answer.
Step 1 ：First, calculate the selling price of the shirts. Harry sells the shirts at a 60% markup based on cost, so the selling price is the cost price plus 60% of the cost price. The cost price is $9.90, so the selling price is \(9.90 + 0.60 \times 9.90 = \$15.84\).
Step 2 ：Next, calculate the gross margin for the 800 shirts sold at the markup price. The gross margin is the selling price minus the cost price. So, the gross margin for the 800 shirts is \(800 \times (15.84 - 9.90) = \$4752.00\).
Step 3 ：Then, calculate the selling price of the remaining 200 shirts. Harry sells these shirts at a 30% reduction from the selling price, so the new selling price is the original selling price minus 30% of the original selling price. So, the new selling price is \(15.84 - 0.30 \times 15.84 = \$11.09\).
Step 4 ：Finally, calculate the gross margin for the 200 shirts sold at the reduced price. The gross margin is the new selling price minus the cost price. So, the gross margin for the 200 shirts is \(200 \times (11.09 - 9.90) = \$237.60\).
Step 5 ：The total gross margin is the sum of the gross margin for the 800 shirts sold at the markup price and the gross margin for the 200 shirts sold at the reduced price. So, the total gross margin is \(4752.00 + 237.60 = \$4989.60\).
Step 6 ：\(\boxed{\$4989.60}\) is the final answer.
