Directions: Solve the following mathematical problem and select the correct option.

A retailer bought a laptop and a tablet. The cost price of the laptop is $1,200 more than the cost price of the tablet. He sold the laptop at a profit of 25% and the tablet at a profit of 10%. If the difference between the selling prices of the laptop and the tablet is $2,100, what is the cost price of the laptop?

The correct option is $5,200.

Step-by-step Explanation:

To find the cost price of the laptop, let us set up the problem by defining the variables for the cost prices of both the laptop and the tablet.

Let $T$ be the cost price of the tablet in dollars.

According to the given information, the cost price of the laptop is $1,200 more than the cost price of the tablet. Therefore, the cost price of the laptop ($L$) can be written as:

$L=T+1200$

Step 1: Calculate the selling prices of both items

The selling price (SP) of an item sold at a profit is calculated by multiplying its cost price by $(1+\text{profit percentage})$.

1. Laptop Selling Price:
The laptop is sold at a profit of 25%. Thus, its selling price is 125% of its cost price:

${\mathrm{SP}}_{\text{laptop}}=1.25\times L$

Substitute $L=T+1200$ into the equation:

${\mathrm{SP}}_{\text{laptop}}=1.25\times (T+1200)$

${\mathrm{SP}}_{\text{laptop}}=1.25T+1500$

2. Tablet Selling Price:
The tablet is sold at a profit of 10%. Thus, its selling price is 110% of its cost price:

${\mathrm{SP}}_{\text{tablet}}=1.10\times T=1.10T$

Step 2: Formulate the equation using the given difference in selling prices

We are given that the difference between the selling prices of the laptop and the tablet is $2,100:

${\mathrm{SP}}_{\text{laptop}}-{\mathrm{SP}}_{\text{tablet}}=2100$

Substitute the expressions for ${\mathrm{SP}}_{\text{laptop}}$ and ${\mathrm{SP}}_{\text{tablet}}$:

$(1.25T+1500)-1.10T=2100$

Step 3: Solve for the cost price of the tablet ($T$)

Combine like terms:

$0.15T+1500=2100$

Subtract 1,500 from both sides of the equation:

$0.15T=2100-1500$

$0.15T=600$

Divide both sides by 0.15:

$T=\frac{600}{0.15}=4000$

The cost price of the tablet is $4,000.

Step 4: Find the cost price of the laptop ($L$)

Using the relationship $L=T+1200$:

$L=4000+1200=5200$

Therefore, the cost price of the laptop is $5,200.