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
