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A dealer once sold identical cars at a piece of x dollars each (includ

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A dealer once sold identical cars at a piece of x dollars each (includ  [#permalink]

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New post 07 Feb 2019, 12:07
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Difficulty:

  55% (hard)

Question Stats:

58% (02:38) correct 42% (03:19) wrong based on 36 sessions

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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

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Re: A dealer once sold identical cars at a piece of x dollars each (includ  [#permalink]

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New post 07 Feb 2019, 13:23
1
Price of each car be P
After price increment P+2500
total price of each car after tax (P+2500)*8%

Total price before increment P*8%
15*(P+2500)*8%=18*P*8%

which P =12500
New price 12500+2500=15000
ST 8%
Total price 15000*8% =16200


Answer D
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Re: A dealer once sold identical cars at a piece of x dollars each (includ  [#permalink]

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New post 10 Feb 2019, 08:57
1
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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Re: A dealer once sold identical cars at a piece of x dollars each (includ   [#permalink] 10 Feb 2019, 08:57
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