A bedroom suite costs Town \& Country Furniture $\$ 5,000$ less $30 \%$ and $15 \%$. The normal rate of markup on cost is $90 \%$. The suite is marked down $30 \%$ in a Mid-Summer Sale.
4 What is the sale price? (Round your answer to the nearest cent.)
points
What is the sale price? (Round your answer to the nearest cent.)
Skipped
Sale price
$\$$

Step 1 ：Let the original cost of the bedroom suite be \(c\).

Step 2 ：The original price after the $90\%$ markup is \(1.9c\).

Step 3 ：The discounted price after the $5,000$ discount is \(1.9c - 5000\).

Step 4 ：Since the discounted price is $30\%$ and $15\%$ less than the original price, we have the equation: \(1.9c - 5000 = 0.85c\).

Step 5 ：Solving for \(c\), we get \(c \approx 4761.90\).

Step 6 ：The original price is \(1.9c \approx 9047.62\).

Step 7 ：Finally, applying the $30\%$ Mid-Summer Sale discount, we get the sale price: \(0.7(9047.62) \approx 2833.33\).

Step 8 ：\(\boxed{2833.33}\) is the sale price of the bedroom suite.