Question

Alex bought a new skate board at a 20% discount. He paid $72.a) what percent of the original price did he Pay?b) what was the original price?c) how many dollars did Alex save by buying the skate board at a discount?

Answer 1

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

Discount rate (r) = 20% = 0.2

Discounted price (d) = $72

a)

The percentage of the original price (p) Alex paid is calculated as shown below:

`\begin{gathered} DiscountPrice=OriginalPrice-(OriginalPrice* DiscountRate) \\ \Rightarrow d=p-p\cdot r\Rightarrow \\ d=p-pr \\ \text{Substitute the values of d, p \& r into the equation above, we have:} \\ 72=p-p(0.2) \\ 72=p-0.2p \\ 72=0.8p\Rightarrow0.8p=72 \\ 0.8p=72 \\ 0.8p\Rightarrow80\text{ \% of the original price} \\ \\ \therefore Alex\text{ paid 80\% of the original price} \end{gathered}`

b)

The original price is calculated as shown below:

`\begin{gathered} \text{0}.8p=72 \\ p=(72)/(0.8)=90 \\ p=90 \\ \\ \therefore\text{ The original price is \$90} \end{gathered}`

c)

The amount Alex saved is given by the difference between the original price & discounted price. We have:

`\begin{gathered} AmountSaved=90-72=18 \\ AmountSaved=\text{ \$}18 \end{gathered}`