PS Ratio Problem

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

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

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.

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

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)

The answer is D.

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.

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

Thanks