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It costs 10¢ a kilometer to fly and 12¢ a kilometer to drive. If you

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It costs 10¢ a kilometer to fly and 12¢ a kilometer to drive. If you [#permalink]

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New post 02 Nov 2017, 02:39
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It costs 10¢ a kilometer to fly and 12¢ a kilometer to drive. If you travel 200 kilometers, flying x kilometers of the distance and driving the rest, then the cost of the trip in dollars is

(A) 20
(B) 24
(C) 24 – 2x
(D) 24 – .02x
(E) 2,400 – 2x
[Reveal] Spoiler: OA

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Re: It costs 10¢ a kilometer to fly and 12¢ a kilometer to drive. If you [#permalink]

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New post 02 Nov 2017, 04:32
Bunuel wrote:
It costs 10¢ a kilometer to fly and 12¢ a kilometer to drive. If you travel 200 kilometers, flying x kilometers of the distance and driving the rest, then the cost of the trip in dollars is

(A) 20
(B) 24
(C) 24 – 2x
(D) 24 – .02x
(E) 2,400 – 2x


¢(10*x + (200-x)*12)
¢(-2x + (2400)
$(24-.02x)
D
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Re: It costs 10¢ a kilometer to fly and 12¢ a kilometer to drive. If you [#permalink]

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New post 02 Nov 2017, 08:04
10x + (200-x)12
10x + 2400 -12x
2400 - 2x

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Re: It costs 10¢ a kilometer to fly and 12¢ a kilometer to drive. If you [#permalink]

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New post 02 Nov 2017, 08:31
Bunuel wrote:
It costs 10¢ a kilometer to fly and 12¢ a kilometer to drive. If you travel 200 kilometers, flying x kilometers of the distance and driving the rest, then the cost of the trip in dollars is

(A) 20
(B) 24
(C) 24 – 2x
(D) 24 – .02x
(E) 2,400 – 2x


An alternate approach would be to model the question, if you don't know how to set up the algebra.

Pick an easy number for x, that is not an exact split (e.g. 100) or a number from the problem, such as 50.

If x = 50, then it costs 50 x .10 = $5 for the flight portion of the trip.

Then, there are 200 - 50 = 150 kilometers left for the drive portion of the trip, so it costs 150 x .12 = $18 for the drive portion of the trip.

Add the two values to find that when x = 50, the cost of the trip is $23. Now, eliminate choices A and B, which are defined numeric values that do not equal $23.

Then, plug in x = 50 into the remaining choices seeking one that yields $23.

(C) 24 - 2(50) = -76 ; eliminate choice C
(D) 24 - .02(50) = 23 ; keep choice D
(E) 2,400 - 2x = 2,300 ; eliminate choice E

The correct answer is choice D.
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Re: It costs 10¢ a kilometer to fly and 12¢ a kilometer to drive. If you [#permalink]

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New post 05 Nov 2017, 08:22
Bunuel wrote:
It costs 10¢ a kilometer to fly and 12¢ a kilometer to drive. If you travel 200 kilometers, flying x kilometers of the distance and driving the rest, then the cost of the trip in dollars is

(A) 20
(B) 24
(C) 24 – 2x
(D) 24 – .02x
(E) 2,400 – 2x


Since x kilometers represents the flying distance, (200 - x) kilometers represents the driving distance.

Thus, the cost was:

0.10x + 0.12(200 - x) = 0.10x + 24 - 0.12x = 24 - 0.02x

Answer: D
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Re: It costs 10¢ a kilometer to fly and 12¢ a kilometer to drive. If you   [#permalink] 05 Nov 2017, 08:22
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