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Toll bridge

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Toll bridge

by alex.gellatly » Sun Aug 26, 2012 12:33 am
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 east value of x for which this driver can save money by using the sticker?

14
15
16
28
29

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by neelgandham » Sun Aug 26, 2012 2:11 am
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 east value of x for which this driver can save money by using the sticker?

Money paid for two crossings per day without the sticker = 0.75*X + 0.75*X
Money paid for two crossings per day using the sticker = 13 + 0.3X + 0.3X
Since, we want to know the least value of x for which the driver can save money by using the sticker, the total money paid for two crossings per day without the sticker should be JUST greater than the money paid for two crossings per day using the sticker.

0.75*X + 0.75*X >(13 + 0.3X + 0.3X)
1.5*X > 13 + 0.6*X
0.9*X > 13
X > 14.44
So, the minimum value of X is 15.
Anil Gandham
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