Car dealer sales

kobel51 wrote:According to a car dealer's sales report, 1/3 of the cars sold during a certain period were sedans and 1/5 of the other cars sold were station wagons. If N station wagons were sold during that period, how many sedans, in terms of N, were sold?

A) 2N/15
B) 3N/5
C) 5N/3
D) 5N/2
E) 15N/2

Here's an algebraic approach.
Let T = total number of cars sold

1/3 of the cars sold during a certain period were sedans
So, (1/3)(T) = # of cars sold that were sedans
This means (2/3)T = # of cars sold that were NOT sedans

1/5 of the other cars sold were station wagons
In other words, 1/5 of the NON-SEDAN cars were station wagons.
So, (1/5)(2/3)T = # of cars sold that were station wagons

N station wagons were sold
In other words, (1/5)(2/3)T = N

How many sedans, in terms of N, were sold?
We already determined that (1/3)(T) = # of cars sold that were sedans
So, our task here is to use the fact that (1/5)(2/3)T = N in order to determine the value of (1/3)(T) in terms of N.

So, let's take (1/5)(2/3)T = N and slowly make the left-hand-side look like (1/3)(T)

Here's what I mean: (1/5)(2/3)T = N
Multiply both sides by 5 to get: (2/3)T = 5N
Divide both sides by 2 to get: (1/3)T = 5N/2
Perfect, we took the equation (1/5)(2/3)T = N and created an EQUIVALENT equation (1/3)T = 5N/2

This is useful because we already determined that (1/3)(T) = # of cars sold that were sedans
So, we can conclude that [spoiler]5N/2[/spoiler] = # of cars sold that were sedans

Answer: D

Cheers,
Brent

kobel51 wrote:According to a car dealer's sales report, 1/3 of the cars sold during a certain period were sedans and 1/5 of the other cars sold were station wagons. If N station wagons were sold during that period, how many sedans, in terms of N, were sold?

A) 2N/15
B) 3N/5
C) 5N/3
D) 5N/2
E) 15N/2

Here's the INPUT-OUTPUT approach.

Let's first choose a nice number that works well with 1/3 and 1/5.
15 is one such number since.
So, let's say that the car dealer sold 15 cars altogether.

1/3 of the cars sold during a certain period were sedans
So, 1/3 of 15 = 5, so 5 of the cars were sedans
This means 10 cars were NOT sedans

1/5 of the other cars sold were station wagons
1/5 of 10 = 2, so 2 of the cars were station wagons

N station wagons were sold
So, N = 2

How many sedans, in terms of N, were sold?
So, when N = 2, the number of sedans sold = 5
Our job now is to take each answer choice and INPUT N = 2, and see which one yields an OUTPUT of 5 sedans.
A) 2(2)/15 = 4/15 sedans.ELIMINATE
B) 3(2)/5 = 6/5 sedans. ELIMINATE
C) 5(2)/3 = 10/3 sedans. ELIMINATE
D) 5(2)/2 = 5 sedans. KEEP
E) 15(2)/2 = 15 sedans. ELIMINATE

Answer: D

Cheers,
Brent