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PS Ratio Problem

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PS Ratio Problem

by Riggz » Sat Mar 01, 2008 9:44 pm
The ratio of buses to cars on River Road is 2 to 23. If there are 630 fewer buses than cars on River Road, how many cars are on River Road?

a)30
b)60
c)660
d)690
e)750

Can someone pls explain this one to me? Explanation is not clear to me.
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by iwillmakeit » Sat Mar 01, 2008 9:55 pm
B/C = 2/23

B = C - 630

Solve both to arrive at the answer.

(C-630)/C = 2/23

1 - 630/C = 2/23

230/C = 21/23

C = 630*23/21 = 690
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by yozero » Sun Mar 02, 2008 3:22 am
well, i think the answer should be "B"

2(x)+630=23(x)
21(x)=630
x=30

since the ratio of bushes to car is 2(x):23 (x)
then the number of bushes is 2(30) = 60
YOZERO
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by Riggz » Sun Mar 02, 2008 8:05 am
correct answer is D 690. thanks iwillmakeit

explanation didnt show the two equations.

yozero u are almost correct lol. It asks for number of cars not buses. But can you please explain how you dervied the equation 2x + 630 = 23x? This is how mgmat has the explanation as well.
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by dgmat » Wed Mar 12, 2008 2:07 pm
Okay this is how I see it.

Cars (C), Buses (B)

B = C - 630 (Buses 630 less than car)

=> 2/23 = B/C or 2/23 = (C - 630) / C
=> 2C = 23C - 14490
=> C= 14490/21
=> C= 690
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by tmmyc » Wed Mar 12, 2008 4:32 pm
Riggz wrote:But can you please explain how you dervied the equation 2x + 630 = 23x? This is how mgmat has the explanation as well.
The question states that the ratio of buses to cars is 2 to 23.

This means there might be 2 buses and 23 cars,
or 4 buses and 46 cars,
or 6 buses and 69 cars,
etc.

Hence, there are
2(x) buses and 23(x) cars
where x is some positive integer.

Next, the question states there are 630 fewer buses than cars. This means the number of buses plus 630 will equal the number of cars.

We already know the number of buses from the previous statement: 2(x)
We also know the number of cars: 23(x)

Translating all the statements into one mathematical equation gives you

2(x) + 630 = 23(x)
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by yalephd2007 » Sun Apr 13, 2008 9:04 am
The answer is D.
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by dalwow » Wed Apr 16, 2008 12:48 pm
Maybe this is overkill for this problem, but I worked this out in a way that seemed quite simple. The difference from cars/buses is 21. The total difference is 630. 630/21 =30. This is the number of buses. Multiply 30*23(which is the number of cars vs. the 30 buses we know we have) and we get 690. To me this looks like an easy way to work it out. Please point it out if I'm wrong, thanks.
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by netigen » Wed Apr 16, 2008 1:04 pm
dalwow wrote:Maybe this is overkill for this problem, but I worked this out in a way that seemed quite simple. The difference from cars/buses is 21. The total difference is 630. 630/21 =30. This is the number of buses. Multiply 30*23(which is the number of cars vs. the 30 buses we know we have) and we get 690. To me this looks like an easy way to work it out. Please point it out if I'm wrong, thanks.
You are not doing anything wrong but just solving the following two equations:

Bus/Car = 2/23
Car = Bus+630

if you solve these two, you get Car = 23 * 30
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by dalwow » Thu Apr 17, 2008 5:12 am
Thanks
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