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# A dealership purchased a car and a truck and then sold them both. The

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Math Expert
Joined: 02 Sep 2009
Posts: 55801
A dealership purchased a car and a truck and then sold them both. The  [#permalink]

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21 May 2019, 00:23
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Difficulty:

45% (medium)

Question Stats:

70% (03:25) correct 30% (03:05) wrong based on 10 sessions

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A dealership purchased a car and a truck and then sold them both. The purchasing cost of the truck was $8,000 greater than the purchasing cost of the car, and the selling price of the truck was$12,000 greater than the selling price of the car. The profit that the dealership made on the car was equal to 20 percent of its purchasing cost, and the profit that the dealership made on the truck was equal to 30 percent of its purchasing cost. If x is the purchasing cost, in dollars, of the car, then x satisfies which of the following equations? (Note: Profit equals selling price minus purchasing cost.)

A. $$0.3x+8,000=0.2x+12,000$$

B. $$1.3x+8,000=1.2x+12,000$$

C. $$0.3(x+8,000)=0.2x+12,000$$

D. $$1.3(x+8,000)=1.2x+12,000$$

E. $$1.3(x+8,000)+12,000=1.2x$$

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Intern
Joined: 29 May 2018
Posts: 7
Re: A dealership purchased a car and a truck and then sold them both. The  [#permalink]

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21 May 2019, 01:16
We start by forming equations from the question stem.

Purchase Price of car = $x Purchase Price of Truck (Pt)=$8000+x

Selling Price of Car = 1.2x (20% profit on \$x =0.2x so Selling Price = Cost + Profit = x+ 0.2x =1.2x)
Selling Price of Truck = 12000+ 1.2x ------------(1)

Profit on Truck = 30%

SP Truck = (8000+x)+ 0.3(8000+x) = 1.3(8000+x)--------------(2)

From 1 and 2

1.3 (8000 +x) = 12000 + 1.2x

Intern
Joined: 07 May 2016
Posts: 5
A dealership purchased a car and a truck and then sold them both. The  [#permalink]

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21 May 2019, 01:56
I think Option D should be the right Answer. Because

Purchase price of Truck is X + 8000; As Purchase Price of Car is given as X
The selling price of the Car is 1.2X
The Selling Price of the Truck is 1.2X+ 12000
Profit of Truck is

0.3(X+8000) = 1.2X+12000-(X+8000)

or, 0.3(X+8000) + (X+8000) = 1.2X+12000
0r, 1.3(X+8000)= 1.2X+12000. Thus, D option
A dealership purchased a car and a truck and then sold them both. The   [#permalink] 21 May 2019, 01:56
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