Fraction w/no absolute numbers

[Zanardi]

I am currently stuck on this single problem:

In one classroom exactly 1/2 of the seats are occupied. In another classroom with double the seating capacity of the first, exactly 3/4 of the seats are occupied. If the students from both classrooms are transferred into a third empty classroom that has a seating capacity exactly equal to the first two combined, what fraction of the seats in the third classroom are occupied?

Thank you for any assistance.

[Night reader]

1st classrom --> # seats n, occupied n/2
2nd classroom --> # seats 2n, occupied 6n/4
3rd classroom --> # seats (n+2n), occupied (n/2 + 6n/4)
ratio --> (n/2 + 6n/4)/3n=2n/3n=2/3

IOM [spoiler]2/3[/spoiler]

I am currently stuck on this single problem:

In one classroom exactly 1/2 of the seats are occupied. In another classroom with double the seating capacity of the first, exactly 3/4 of the seats are occupied. If the students from both classrooms are transferred into a third empty classroom that has a seating capacity exactly equal to the first two combined, what fraction of the seats in the third classroom are occupied?

Thank you for any assistance.

[gmatmachoman]

X= number of seats in a room.

Room 1 : X

Occupied X/2

Room 2 : 2X

Occupied : 3/4 * 2X = 3/2 X

Combined seating capacity ( Room 3) = Total capacity of Room 1 +Total capacity of Room 2
= X+2X
= 3X

Occupied seats : X/2 + 3/2 X
: 2X

Question asks for fraction of seats occupied over total capacity:

= 2X/ 3X
= 2/3
= 66.6%

[ikaplan]

I would use picking numbers for this one.

First classroom: capacity --> 6, occupied--> 1/2*6= 3
Second classroom: capacity --> 12, occupied --> 3/4*12=9
Third classroom: capacity --> 6+12=18, occupied --> 9+3=12

ratio=12/18=2/3

IMO [spoiler]2/3[/spoiler]

[GMATGuruNY]

I am currently stuck on this single problem:

In one classroom exactly 1/2 of the seats are occupied. In another classroom with double the seating capacity of the first, exactly 3/4 of the seats are occupied. If the students from both classrooms are transferred into a third empty classroom that has a seating capacity exactly equal to the first two combined, what fraction of the seats in the third classroom are occupied?

Thank you for any assistance.

We can plug in values that satisfy the conditions given. Let A = smaller classroom and B = larger classroom.

Plug in A = 2 seats.
Number of seats occupied in A = 1/2 * 2 = 1.
Since B is twice as big as A, B = 2*2 = 4 seats.
Number of seats occupied in B = 3/4 * 4 = 3.
Total seats occupied = 1+3 = 4.
Total seats combined = A+B = 2+4 = 6.
Total occupied/Total seats = 4/6 = 2/3.

[Zanardi]

Thanks for all the replies!