SOLUTION: This is a capacity question. when Memorial Hospital is filled to capacity, it has 18 more people in semiprivate rooms (two patients to a room) than in private rooms. The room ra

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Question 133958: This is a capacity question.
when Memorial Hospital is filled to capacity, it has 18 more people in semiprivate rooms (two patients to a room) than in private rooms. The room rates are $200 per day for a private room and $150 per day for a semiprivate room. If the total receipts for rooms is $17,400 per day when all are full, then how many rooms of each type does the hospital have?
Answer by scott8148(5880) (Show Source):
You can put this solution on YOUR website!
let x="semiprivate rooms" and y="private rooms"

"18 more people in semiprivate rooms (two patients to a room) than in private rooms"
__ 2x=y+18 __ 2x-18=y

" total receipts for rooms is $17,400 per day when all are full"
__ 300x+200y=17400 __ 3x+2y=174

substituting __ 3x+2(2x-18)=174 __ 3x+4x-36=174 __ 7x=210 __ x=30

substituting __ y=2x-18 __ y=2(30)-18 __ y=42