When you receive a loan to make a purchase, you often must make a down payment in cash. the amount of the loan is the purchase cost minus the down payment. riva made a down payment of $1500 on a used car. she received a loan of $2600. write and solve an equation to find the cost of the car.

Summarizing the problem, there are three terms that you have to deal with: purchasing cost, down payment and loan. So, you would expect that the answer would contain these quantities. Among them, the unknown is the purchasing cost, therefore, we denote this as x. 

Based on the statement, "The amount of the loan is the purchase cost minus the down payment", we can formulate an equation for this. 

Amount of Loan = x - Down payment

This will be our working equation. Moving on, the down payment was mentioned to be equal to $1500. The lean received is equal to $2600. Substituting these values to the working equation, we can now determine the value of x.

2600 = x - 1500

Solving for x by transposing it to one side,

x = 2600-1500
x = $1,100

Therefore, the purchasing cost of the car is $1,100.