Question

You are looking for a new car and the dealer claims the price of the model you like has been reduced by \(\$ 1150 .\) The window sticker shows the new price as \(\$ 12,985 .\) a. Represent the original price by a letter and then write an equation for the new price. b. Solve your equation to determine the original price. (Remember to check your result as a last step.)

Short answer

Answer: The original price of the car was $14,135.

Step-by-step solution

Represent the original price by a letter

Let the original price be represented by the letter \(x\).

Write an equation for the new price

Since the price was reduced by $1,150, the equation to represent the new price would be: \(x - 1150 = 12985\) b. Solve the equation and check the result.

Solve the equation

To solve the equation \(x - 1150 = 12985\), add \(1150\) to both sides: \(x - 1150 + 1150 = 12985 + 1150\) \(x = 14135\) So, the original price of the car was \(14,135\).

Check the result

To verify if our solution is correct, subtract \(1,150\) from the original price and make sure it's equal to the new price: \(14135 - 1150 = 12985\) The price matches the new price given, so the original price of the car is indeed \(14,135\).