1. **Problem statement:** We want to find the labeled price $x$ of a dress such that after giving a 20% discount, the seller still makes a 25% profit on the cost price of 80. 2. **Understanding the problem:** - The cost price (CP) is 80. - The seller wants a 25% profit, so the selling price (SP) should be $1.25 \times 80$. - The labeled price is $x$, but the dress is sold at 20% discount, so the actual selling price is $0.8 \times x$. 3. **Set up the equation:** $$0.8 \times x = 1.25 \times 80$$ 4. **Solve for $x$:** $$x = \frac{1.25 \times 80}{0.8}$$ 5. **Calculate the value:** $$x = \frac{100}{0.8} = 125$$ 6. **Interpretation:** The labeled price should be 125 to ensure a 25% profit after a 20% discount. **Final answer:** $x = 125$