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

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ajit257
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The toll for crossing a certain bridge is $0.75 each crossin [#permalink] New post   03 Jan 2011, 18:22
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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
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Bunuel
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Re: The toll for crossing a certain bridge [#permalink] 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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Burnkeal
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Re: The toll for crossing a certain bridge [#permalink] New post   04 Jan 2011, 01:03
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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] 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] New post   11 Feb 2013, 19:19
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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] 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] 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] New post   24 Jan 2018, 10:40
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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


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] New post   13 Nov 2021, 07:21
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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


In other words, we want to find the value of x such that: (total payments WITH sticker) < (total payments WITHOUT sticker)

total payments WITHOUT sticker
If the driver crosses the bridge twice on x days, but then the total number of crossings = 2x
Since each crossing will cost $0.75, the total payments for the month = (2x)($0.75) = 1.5x

Total payments WITH sticker
The sticker costs $13.00
If the driver crosses the bridge twice on x days, but then the total number of crossings = 2x
Since each crossing will cost $0.30, the total payments for the month = $13.00 + (2x)($0.30) = 13.00 + 0.6x


So, our inequality becomes: 13.00 + 0.6x < 1.5x
Subtract 0.6x from both sides: 13 < 0.9x
Divide both sides by 0.9 to get approximately: 14.44 < x

Since x must be a positive integer, the smallest 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] New post   18 Apr 2022, 02:41
Hi all, can anyone explain when 14.44 < x, why is not 14 but 15? Thanks
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Re: The toll for crossing a certain bridge is $0.75 each crossin [#permalink] New post   08 Jul 2023, 06:04
I converted all given values to cents to get rid of the decimals.

Without sticker:
75 cents x 2 trips = 150 cents per day

With sticker (which cost 1300 cents):
30 cents x 2 trips = 60 cents per day

Quote:
... what is the least value of x for which this driver can save money by using the sticker?


The question wants to know at how many trips the driver, by using the sticker, would break even and start experiencing savings.

Cost w/o sticker = Cost w/ sticker
150x = 1300 + 60x
90x = 1300
x = 14.4

Since x has to be an integer and rounding down would mean that he doesn't break even, we need to round up.

Therefore, x = 15.
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Re: The toll for crossing a certain bridge is $0.75 each crossin [#permalink]
08 Jul 2023, 06:04
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