SajjadAhmad wrote:
A dealer once sold identical cars at a piece of x dollars each (including sales tax). However, the pre-tax price was recently increased by $2,500 such that 18 cars purchased at the old price would cost the same as purchasing three fewer cars at the new price. If the sales tax rate is 8% , what is the new price of the dealer's cars, including sales tax, in dollars?
A) $10,800
B) $12,500
C) $13,500
D) $16,200
E) $16,750
Since the sales tax rate is 8%, the original pre-tax price of the car is x/1.08, and the new pre-tax price of the car is therefore x/1.08 + 2500. We know that 18 cars at the old price is equivalent to 15 cars at the new price. Thus, we can create the equation:
18x = (x/1.08 + 2500)(1.08)(15)
18x/15 = (x/1.08 + 2500)(1.08)
1.2x = x + 2700
0.2x = 2700
x = 13,500
Therefore, the new price of the car, including sales tax, is (13,500/1.08 + 2500)(1.08) = 13,500 + 2,700 = 16,200 dollars.
Answer: D
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