Question

Pep Boys Automotive paid $208.50 for a pickup truck bed liner. The original selling price was $291.90, but this was marked down 35%. If operating expenses are 28% of the cost, find the absolute loss

Answer 1

Step 1: State the given in the question

THe following were given:

`\begin{gathered} \text{Amount Paid (}A_{\text{paid}})=208.50 \\ (Originalsellingprice)SP_(ORIGINAL)=291.90 \\ \text{Marked Percentage=35\%} \\ \text{Operating expenses=28\%} \end{gathered}`

Step 2: State what is to be found

We are to find the absolute loss

Step 3: Calculate the selling price

Please note that the selling price is the marked down price

The marked down price would be

`\begin{gathered} P_{\text{MARKED DOWN}}=(100-35)\text{ \% of original selling price} \\ P_{\text{MARKED DOWN}}=65\text{ \% of }SP_(ORIGINAL) \\ P_{\text{MARKED DOWN}}=(65)/(100)*291.90=189.74 \end{gathered}`

The selling price is the marked down price which is $189.74

Step 4: Calcualte the operating expenses

Please note that the cost price is amount paid. Therefore, the operating expenses would be as calculated below:

`\begin{gathered} E_{\text{OPEARATING}}=28\text{ \% of Amount Paid} \\ E_{\text{OPERATING}}=28\text{ \% of }A_{\text{paid}}=(28)/(100)*208.50 \\ E_{\text{OPERATING}}=0.28*208.50=58.38 \end{gathered}`

Hence, the operating expenses is $58.38

Step 5: Calculate the total cost price

The total cost price is the addition of the cost price and the operating expenses. This is as calculated below:

`\begin{gathered} C_{\text{TOTAL COST PRICE}}=E_(OPERATING)+A_(PAID) \\ C_{\text{TOTAL COST PRICE}}=58.38+208.50=266.88 \end{gathered}`

Hence, the total cost price is $266.88

Step 6: Calculate the absolute loss

The absolute loss is the difference between the total cost price and the marked down price (or the actual selling price). This is as calculated below:

`\begin{gathered} L_{\text{ABSOLUTE LOSS}}=C_{TOTAL\text{ COST PRICE}}-P_{MARKED\text{ DOWN}} \\ L_{\text{ABSOLUTE LOSS}}=266.88-189.74=77.14 \end{gathered}`

Hence, the absolute loss is $77.14