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The toll for crossing a certain bridge is $0.75 each crossing. Drivers

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GeminiHeat
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The toll for crossing a certain bridge is $0.75 each crossing. Drivers [#permalink] New post   16 Nov 2021, 08:23
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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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Re: The toll for crossing a certain bridge is $0.75 each crossing. Drivers [#permalink] New post   16 Nov 2021, 09:38
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GeminiHeat 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 crossing. Drivers [#permalink]
16 Nov 2021, 09:38
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