Question

A store is offering a 20% discount on all items. Is there a proportional relationship between the original price of an item and its price after the discount? Yes or no.

Answer 1

Let's begin by identifying key information given to us:

Discount (d) = 20% = 0.2

Price (before discount) = P

Price after discount (Q) is calculated thus:

`\begin{gathered} Q=P-P\cdot d \\ d=0.2 \\ \Rightarrow Q=P-0.2P \\ Q=0.8P=\text{ 80\%(P)} \\ \\ \end{gathered}`

As such, Yes there is a proportional relationship between the original price of an item and its price after the discount.

A discount of 20% implies that you are paying 80% of the original price

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