olivite wrote:
A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 3 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?
A. 11/30
B. 29/60
C. 17/30
D. 19/30
E. 11/15
I don't understand how can you infer from the sentence "the number of beds available for patients at the hospital is now 3 times the number available before the new tower was built" that the "The new tower is not itself three times the size of the old wing; the problem states that the capacity of the entire hospital is three times its original value, so the new tower has twice as many beds as the old wing"
I keep re-reading the sentece and still see that the new hospital is 3 times bigger than the old one.
HELP
Given:
1. A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 3 times the number available before the new tower was built.
2. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied.
3. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower.
Asked: If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?
Let the number of beds originally be x
Number of beds after a new tower is built = 3x
Number of beds in new tower = 3x-x = 2x
Occupied beds: -
x/3 original beds
2x/5 beds in new tower
Since all patients in original beds are transferred to new tower
Occupied beds in new tower will become = x/3 + 2x/5 = 11x/15
Fraction of beds occupied in new tower = 11x/15 / 2x = 11/30
Fraction of beds unoccupied in new tower = 1 - 11/30 = 19/30
IMO D