Q50. - Algebra 1

Question

SHORT RESPONSE Maddie works at Game Exchange. They are having a sale as shown.

She purchases four video games and uses her employee discount of $15\%$. If sales tax is $7.25\%$, how much does she spend on the games?

 

Step-by-Step Solution

Answer

Maddie spends $54.7 on video games.

Step 1. State the formula.

The selling price of an object is given as,

$SP=\left(1-\frac{d}{100}\right)\left(1+\frac{ST}{100}\right)CP$, where $SP$ is the selling price, d is the discount percentage, $ST$ is the sales tax and $CP$ is the cost price.

Step 2. List the given data.

There is a sale on video games with the offer of “Buy 2 get 1 free”. The cost price of a video game is $20. Employee discount is $15\%$ and sales tax is $7.25\%$.

Then, $d=15$ and $ST=7.25$.

Step 3. Calculate the.

Maddie purchases 4 video games. There is an offer of “Buy 2 get 1 free” on video games. Then, the third video game is free and Maddie effectively purchases 3 games.

 

The cost price of one video game is $20. Then, the cost price of 3 video games is $60.

 

So, $CP=60$.

 

Put $d=15$, $ST=7.25$ and $CP=60$ in $SP=\left(1-\frac{d}{100}\right)\left(1+\frac{ST}{100}\right)CP$ to get,

$$\begin{gathered} SP=\left(1-\frac{15}{100}\right)\left(1+\frac{7.25}{100}\right)60 \\ =\left(1-0.15\right)\left(1+0.0725\right)60 \\ =\left(0.85\right)\left(1.0725\right)60 \\ =54.6975 \end{gathered}$$

So, $SP=54.6975$

Rounding off to nearest tenth, $SP=54.7$.

 

So, Maddie spends $54.7 on video games.