a new tower has just been built at the verbico military hospital ; the number of beds available for patients at the hospital is now 7 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 ?
"i think a - 67 / 90 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 7 x so old = x , new = 6 x now 1 / 3 of x are occupied and 1 / 5 of 6 x are occupied which simplifies to ( 6 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 6 / 5 of x occupied in the new ward . add them up to get 23 / 15 of x there are 6 x beds in new tower so ratio is : ( 23 / 15 ) x / 6 x = 23 / 90 of x subtract that from 90 / 90 of x and you get the number of un - occupied beds to total capacity of new tower = 67 / 90 . a"
multiply(add(multiply(7, 3), 1), multiply(divide(1, 3), divide(1, 5)))