Question

1. noah has a coupon for 30% off at his favorite clothing store. he uses it to buy a hoodie and a pair of jeans.

a. noah paid $28 for the jeans after using the coupon. what is the regular price of the jeans?
b. the regular price of a hoodie is $27. what did noah pay for the hoodie?
c. if the regular price of an item is x dollars, what is the discounted price, in dollars?

Explanation:

Part a

Step1: Define variable for regular price

Let \( r \) be the regular price of the jeans. A 30% off means Noah pays \( 100\% - 30\% = 70\% \) of the regular price. So the equation is \( 0.7r = 28 \).

Step2: Solve for \( r \)

Divide both sides by \( 0.7 \): \( r=\frac{28}{0.7}=40 \).

Step1: Calculate discount amount

The discount is 30% of \(\$27\), so discount \( = 0.3\times27 = 8.1 \).

Step2: Find the paid price

Paid price \( = 27 - 8.1 = 18.9 \). Or, since he pays 70% of regular price: \( 0.7\times27 = 18.9 \).

Step1: Determine the percentage paid

After 30% off, the percentage of regular price paid is \( 1 - 0.3 = 0.7 \).

Step2: Write the discounted price formula

If regular price is \( x \), discounted price \( = 0.7x \) (or \( \frac{7}{10}x \) or \( 70\% \) of \( x \)).

Answer:

The regular price of the jeans is \(\$40\).

Part b