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On a certain road, 10 % of the motorists exceed the posted

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On a certain road, 10 % of the motorists exceed the posted [#permalink] New post 16 Oct 2008, 12:48
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On a certain road, 10 % of the motorists exceed the posted speed limit and receive speeding tickets, but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?

a. 10.5%
b. 12.5%
c. 15%
d. 22%
e. 30%


I could not find any way of answering this question, could someone explain how this question is answered
TC 25
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Re: PS: Percentages [#permalink] New post 16 Oct 2008, 14:34
0.1+0.2x=x
x=1/8=12.5%

Explanation:
Let x be the number of ppl exceeding the speed limit
motorists who exceed the posted speed limit do not receive speeding tickets =0.2x
motorists exceed the posted speed limit and receive speeding tickets = 0.1

Therefore, total exceed = Those who exceed and don't recieve ticket + Those who exceed and recieve ticket.
0.1+0.2x=x

It will be easier to visualize if you draw a 2x2 grid with recived tickets/not recieved tickets Vs exceeded/not exceeded.

One needs to be careful dealing with these problems containing statements like these:
1) "but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets" - gives 0.1+0.2x=x => 12.5%
2) "but 20% of the motorists exceed the posted speed limit and they do not receive speeding tickets" - gives 0.1+0.2=0.3 =>30%
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Re: PS: Percentages [#permalink] New post 16 Oct 2008, 16:10
[quote="hbs2012"]On a certain road, 10 % of the motorists exceed the posted speed limit and receive speeding tickets, but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?

a. 10.5%
b. 12.5%
c. 15%
d. 22%
e. 30


1000 ON THE ROAD, 100 EXCEEDS AND RECIEVES, 100 = 0.8 X , X = 125 who EXCEDDS SPEED LIMIT BOTH ( RECEIVES AND NOT)

125/1000 = 12.5%..........b
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Re: PS: Percentages [#permalink] New post 16 Oct 2008, 16:12
hbs2012 wrote:
On a certain road, 10 % of the motorists exceed the posted speed limit and receive speeding tickets, but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?

a. 10.5%
b. 12.5%
c. 15%
d. 22%
e. 30%


I could not find any way of answering this question, could someone explain how this question is answered
TC 25


answer 12.5%
100 motorist on the road and 10 motorist got tickets.
20% of the motorist who exceeded speed limit (say X number of motorist) did not get tickets, that means 80% of the motorist who exceeded speed limits got tickets
therefore we have the following equation.
80% X=.1
x=12.5%
Re: PS: Percentages   [#permalink] 16 Oct 2008, 16:12
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