set up a 2 by 2 matrix, let there be 100 motorists

let x motorists exceed limit, 10 exceeded limit and received ticket.
=>exceeded limit but not ticketed: x-10

x-10=20%*x
solving x=25/2=12.5%

hence, B

You have two groups:
- motorists who exceed the speed limit - call them a
- motorists who do not exceed the speed limit - call them b

You have that a + b = t (total motorists).

Out of group a, you'll also have two subgroups:
- speeders who get tickets - call them x
- speeders who don't get tickets - call them y.

x + y = a.

Now, 10% of motorists exceed the speed limit and get tickets, meaning that 10% of t are part of this other group, so 0.1*t = x.
20% of the motorists who exceed the speed limit don't get tickets, meaning that 0.2*a = y.

You're looking for a relationship between a and t.

Replace x and y in x + y = a to get:

0.1t + 0.2a = a
0.1t = 0.8a
t = 8a
a = t/8 = 0.125 * t = 12,5 * t.

thank you

Can't you pick numbers at this problem?

scoobydooby solved this problem by picking numbers. I'm actually considering writing my own version of "picking numbers strategy guide", since I see most people really like this method.... What do you think? Would you be interested in seeing such a post?

Yes it would be nice DanaJ. I really like the picking numbers, because it makes me pace .


I picked 100 as a total score but I got a answer of 28%.


100 x 0.10 = 10 ( who exceeded the posted speed limit and receive speeding tickets )

90 x 0.20 = 18 ( who exceeded the posted speed limit do not receive speeding tickets )

28 / 100 = 28 %

What did I wrong at my calculation?