Question

problem 12: spiral review
bettie’s boutique is having a 20% off sale.
here is the table from the previous screen.
explain why the relationship between original price and sale price is proportional.

item	original price	sale price (dollars)
tie	$25	20
scarf	$35	28

Explanation:

Step1: Calculate sale price ratio

$\frac{\text{Sale Price}}{\text{Original Price}}$ for Hat: $\frac{12}{15}=0.8$

Step2: Calculate second item's ratio

$\frac{\text{Sale Price}}{\text{Original Price}}$ for Tie: $\frac{20}{25}=0.8$

Step3: Calculate third item's ratio

$\frac{\text{Sale Price}}{\text{Original Price}}$ for Scarf: $\frac{28}{35}=0.8$

Step4: Verify proportionality

A relationship is proportional if the ratio of the two quantities is constant. All ratios equal 0.8, and the sale price can be written as $\text{Sale Price}=0.8\times\text{Original Price}$, which fits the form $y=kx$ (proportional equation).

Answer:

The relationship is proportional because the ratio of sale price to original price is a constant 0.8 for all items, and the sale price is equal to 80% (100% - 20%) of the original price, following the proportional form $y = kx$ where $k=0.8$.