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

Question

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

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

Bunuel · Accepted Answer

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.

Burnkeal · Answer

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?

denver · Answer

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

sambam · Answer

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

mau5 · Answer

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.

usre123 · Answer

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

JeffTargetTestPrep · Answer

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

BrentGMATPrepNow · Answer

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

Kimberly77 · Answer

Hi all, can anyone explain when 14.44 < x, why is not 14 but 15? Thanks

achloes · Answer

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

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.

KarishmaB · Answer

By paying $13, the driver will save $0.45 each crossing. 
After how many crossings will he break even? After 13/0.45 = 28.something crossings.

Since he crosses twice a day, he will not break even till the 14th day. On the 15th day, on his 29th crossing he would have broken even and would have saved money. 
Hence he can say money if x is at least 15.

Answer (B)

KinshuIdnani · Answer

0.75x > 13 + 0.30x
0.75x - 0.30x > 13
0.45x > 13
x > 28.88

However, remember that 28.88 represents the number of crossings he will need to make to recover those $13, crossing 2 times a day.

So, for days => 28.88 ?? 2 = 14.44.

Thus, 14.44 is the minimum number of days it will take to recover the $13 monthly sticker cost. Therefore, for minimum days, round up to the next nearest whole number, which is 15 days.

bumpbot · Answer

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

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