Question

An item originally costs $175.00. The item is now on sale for $99.75. What percentis the sale price of the original price? Is this an example of percent increase ordecrease? Explain how you know.*

Answer 1

Let:

Op = Original price

Dp = Discount price

r = percent of discount

The discount price will be, the original price minus the product of the original price and the percent of discount, so:

$\begin{gathered} Dp=Op-Op\cdot r \\ where \\ Op=175 \\ Dp=99.75 \\ 99.75=175-175\cdot r \\ 175\cdot r=175-99.75 \\ 175\cdot r=75.25 \\ r=\frac{75.25}{175} \\ r=0.43 \end{gathered}$

The percent of discount of the item is 43%