Madeline goes to a store and buys an item that costs $x$ dollars. She has a coupon for $15 \%$ off, and then a $4 \%$ tax is added to the discounted price. Write an expression in terms of $x$ that represents the total amount that Madeline paid at the register. $\newline$ Answer:

Full solution

Q. Madeline goes to a store and buys an item that costs

x

dollars. She has a coupon for

15 \%

off, and then a

4 \%

tax is added to the discounted price. Write an expression in terms of

x

that represents the total amount that Madeline paid at the register.

\newline

Answer:

Calculate Discount Amount: First, we need to calculate the discount amount that Madeline gets with her coupon. The discount is $15\%$ of the original price $x$ . $\newline$ Discount Amount = Original price $\times$ Discount percentage $\newline$ = $x \times \frac{15}{100}$ $\newline$ = $x \times 0.15$
Find Discounted Price: Next, we subtract the discount amount from the original price to find the discounted price Madeline has to pay before tax. $\newline$ Discounted price = Original price - Discount Amount $\newline$ = $x - (x \times 0.15)$ $\newline$ = $x - 0.15x$ $\newline$ = $0.85x$
Calculate Tax Amount: Now, we need to calculate the tax amount that will be added to the discounted price. The tax is $4\%$ of the discounted price. $\newline$ Tax Amount = Discounted price $\times$ Tax percentage $\newline$ = $0.85x \times \frac{4}{100}$ $\newline$ = $0.85x \times 0.04$ $\newline$ = $0.034x$
Calculate Total Cost: Finally, we add the tax amount to the discounted price to find the total amount Madeline paid at the register. $\newline$ Total cost = Discounted price + Tax Amount $\newline$ = $0.85x + 0.034x$ $\newline$ = $0.884x$