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The toll for crossing a certain bridge is $0.75 each crossin

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The toll for crossing a certain bridge is $0.75 each crossin [#permalink]

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New post 03 Jan 2011, 18:22
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A
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D
E

Difficulty:

  75% (hard)

Question Stats:

56% (02:03) correct 44% (01:49) wrong based on 430 sessions

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The toll for crossing a certain bridge is $0.75 each crossing. Drivers who frequently use the bridge may instead purchase a sticker each month for $13.00 and then pay only $0.30 each crossing during that month. If a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day, what is the least value of x for which this driver can save money by using the sticker?

A. 14
B. 15
C. 16
D. 28
E. 29
Spoiler: OA

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Re: The toll for crossing a certain bridge [#permalink]

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New post 04 Jan 2011, 01:03
1
I don't get this one. I would do for D. I plugged the number of the OA in my equation but it does not work for me.

Anyone?
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Re: The toll for crossing a certain bridge [#permalink]

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New post 04 Jan 2011, 03:50
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ajit257 wrote:
The toll for crossing a certain bridge is $0.75 each crossing. Drivers who frequently use the bridge may instead purchase a sticker each month for $13.00 and then pay only $0.30 each crossing during that month. If a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day, what is the least value of x for which this driver can save money by using the sticker?
A. 14
B. 15
C. 16
D. 28
E. 29


Cost for the driver for 2x (twice on each of x days) crosses without the sticker will be: \(2x*0.75\);
Cost for the driver for 2x (twice on each of x days) crosses with the sticker will be: \(13+2x*0.3\);

Question: what is the least value of \(x\) for which \(13+2x*0.3<2x*0.75\) --> \(x>14.4\) --> \(x_{min}=15\).

Answer: B.
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Re: The toll for crossing a certain bridge [#permalink]

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New post 04 Jan 2011, 09:16
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Savings per crossings = 0.45 (.75-.30)

Saving per crossing x 2 times (crossing bothways) x Number of days >= $13

(.45)2x>=13
.9x>=13
x>14.44

Xmin =15 days
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Re: Arithematic [#permalink]

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New post 11 Feb 2013, 19:19
Option #1: $0.75/crossing....Cross twice a day = $1.5/day
Option #2: $0.30/crossing....Cross twice a day = $0.6/day + $13 one time charge.

If we go down the list of possible answers, you can quickly see that 14 days will not be worth purchasing the sticker. 1.5x14 (21) is cheaper than 0.6x14 +13 (21.4)...it's pretty close so let's see if one more day will make it worth it... If we raise the number of days to 15, the sticker option looks like a better deal...1.5x15 (22.5) vs 0.6x15 + 13 (22). Answer: B
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Re: Arithematic [#permalink]

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New post 11 Feb 2013, 22:59
For the given condition,

\(0.3*2*x+13<0.75*x*2\)

or

\(0.6*x+13<1.5*x\)

or \(0.9*x>13\)

\(x>130*0.11\) = 14.3

Thus x = 15.

B.
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Re: The toll for crossing a certain bridge is $0.75 each crossin [#permalink]

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New post 09 Nov 2014, 11:19
make equations!
For what value of x would the following be true:0.75*2*x> 0.3*2*x +13.
x>14.4, or 15 days.
B
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Re: The toll for crossing a certain bridge is $0.75 each crossin [#permalink]

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New post 24 Jan 2018, 10:40
ajit257 wrote:
The toll for crossing a certain bridge is $0.75 each crossing. Drivers who frequently use the bridge may instead purchase a sticker each month for $13.00 and then pay only $0.30 each crossing during that month. If a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day, what is the least value of x for which this driver can save money by using the sticker?

A. 14
B. 15
C. 16
D. 28
E. 29


We can create the following inequality:

0.75(2x) > 13 + 0.3(2x)

1.5x > 13 + 0.6x

0.9x > 13

x > 13/0.9

x > 130/9

x > 14 4/9

So the minimum value of x is 15.

Answer: B
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Re: The toll for crossing a certain bridge is $0.75 each crossin   [#permalink] 24 Jan 2018, 10:40
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