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A parking lot charges a flat rate of X dollars for any amount of time

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A parking lot charges a flat rate of X dollars for any amount of time [#permalink]

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New post 16 Oct 2017, 01:28
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Question Stats:

79% (01:11) correct 21% (16:02) wrong based on 77 sessions

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A parking lot charges a flat rate of X dollars for any amount of time up to two hours, and X/6 for each hour or fraction of an hour after the first two hours. How much does it cost to park for 5 hours and 15 minutes?

(A) 3X
(B) 2X
(C) 5X/3
(D) 3X/2
(E) 7X/6

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Re: A parking lot charges a flat rate of X dollars for any amount of time [#permalink]

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New post 17 Oct 2017, 11:55
Bunuel wrote:
A parking lot charges a flat rate of X dollars for any amount of time up to two hours, and X/6 for each hour or fraction of an hour after the first two hours. How much does it cost to
park for 5 hours and 15 minutes?

(A) 3X
(B) 2X
(C) 5X/3
(D) 3X/2
(E) 7X/6


For the first two hours, the parking lot charges X dollars. For the remaining 3 hours and 15 minutes, the parking lot will charge the same as it would if the car were parked for 4 hours; thus, it charges 4(X/6) = 4X/6 = 2X/3 dollars. Thus, the total cost for parking the car for 5 hours and 15 minutes is:

X + 2X/3 = 3X/3 + 2X/3 = 5X/3 dollars

Answer: C
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Re: A parking lot charges a flat rate of X dollars for any amount of time [#permalink]

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New post 17 Oct 2017, 18:24
1
Parking lot charges for first two hours= X
Parking lot charges for the remaining 3 hours and 15 minutes= 4*\(\frac{X}{6}\)= \(\frac{2X}{3}\)

Thus, the total cost for parking the car for 5 hours and 15 minutes is:

X+\(\frac{2X}{3}\)= \(\frac{3X+2X}{3}\)= \(\frac{5X}{3}\)

Answer: C.
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Re: A parking lot charges a flat rate of X dollars for any amount of time [#permalink]

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New post 22 Oct 2017, 13:56
1
I did it this way.
-Hours 0 to 2 = x
-Hours 3,4,5 and 6 = 4*[x][/6]
-[4x][/6]+x=[5x][/3]
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Re: A parking lot charges a flat rate of X dollars for any amount of time [#permalink]

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New post 22 Oct 2017, 14:27
Bunuel wrote:
A parking lot charges a flat rate of X dollars for any amount of time up to two hours, and X/6 for each hour or fraction of an hour after the first two hours. How much does it cost to
park for 5 hours and 15 minutes?

(A) 3X
(B) 2X
(C) 5X/3
(D) 3X/2
(E) 7X/6

I chose values.

Let X = $6 (for 2 hours)
X/6 = $1 per hr or part hr > 2

5 hrs 15 minutes costs:

$6 for 2 hours +
$4 for 3+ hours =
$10

Check choices with X = 6, and the answer needs to be 10:

(A) 3X = 18. NO

(B) 2X = 12. NO

(C) 5X/3 = 30/3 = 10. MATCH

(D) 3X/2 = 18/2 = 9. NO

(E) 7X/6 = 42/6 = 7. NO

ANSWER C
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Re: A parking lot charges a flat rate of X dollars for any amount of time [#permalink]

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New post 22 Oct 2017, 15:17
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A parking lot charges a flat rate of X dollars for any amount of time up to two hours, and X/6 for each hour or fraction of an hour after the first two hours. How much does it cost to
park for 5 hours and 15 minutes?

(A) 3X
(B) 2X
(C) 5X/3
(D) 3X/2
(E) 7X/6

---
My 2 cents:
Since the charge is X dollar for the first 2 hours, and X/6 dollars for each hour or fraction of an hour after the first two hour,
i]for the first 2 hours, cost is X dollars
ii] for the next 3hours and 15 minutes, the cost will be X/6 *4 = 4X/6=2X/3 dollars(X/6 is multiplied by 4 since 3 hours and 1 fraction of the fourth hours = 4 time period)
hence for 5 hours and 15 minutes, the cost will be X+2X/3 = 5X/3 dollars.
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Re: A parking lot charges a flat rate of X dollars for any amount of time [#permalink]

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New post 22 Oct 2017, 18:41
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X+(x/6)+(x/6)+(x/6)+(x/6) = 5x/3

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Re: A parking lot charges a flat rate of X dollars for any amount of time [#permalink]

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New post 11 May 2018, 07:34
Top Contributor
Bunuel wrote:
A parking lot charges a flat rate of X dollars for any amount of time up to two hours, and X/6 for each hour or fraction of an hour after the first two hours. How much does it cost to park for 5 hours and 15 minutes?

(A) 3X
(B) 2X
(C) 5X/3
(D) 3X/2
(E) 7X/6


2 hours: cost = x dollars
3 hours: cost = x + x/6 dollars
4 hours: cost = x + x/6 + x/6 dollars
5 hours: cost = x + x/6 + x/6 + x/6 dollars
5.25 hours: cost = x + x/6 + x/6 + x/6 + x/6 dollars

We must now simplify: x + x/6 + x/6 + x/6 + x/6 dollars
Rewrite with common denominator: 6x/6 + x/6 + x/6 + x/6 + x/6 dollars
Combine numerators: 10x/6 dollars
Simplify: 5x/3 dollars

Answer: C

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Brent
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Re: A parking lot charges a flat rate of X dollars for any amount of time   [#permalink] 11 May 2018, 07:34
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