SOLUTION: A travel agent offers two package vacation plans. The first plan costs $360 and includes 3 days at a hotel and a rental car for 2 days. The second plan costs $500 and includes 4 da

Question 87967: A travel agent offers two package vacation plans. The first plan costs $360 and includes 3 days at a hotel and a rental car for 2 days. The second plan costs $500 and includes 4 days at a hotel and a rental car for 3 days. The daily charge for the room is the same under each plan, as is the daily charge for the car. Find the cost per day for the room and for the car. (Please show your system of equations and answer the question in a complete sentence.)
Answer by dolly(163) (Show Source):
You can put this solution on YOUR website!
Let the cost per day for the room be $x and that of the car be $y.
As per the first plan, 3x+2y = 360
As per the second plan, 4x+3y = 500
So the system of equations are
3x+2y = 360 -------------(1)
4x+3y = 500 -------------(2)
This is going to be solved by elimination.
(1) times 3 gives, 9x+6y = 1080
(2) times 2 gives, 8x+6y = 1000
Subtracting the above 2 equations, x = 80
Plugging in this value in (1),
3(80)+2y = 360
240+2y = 360
==> 2y = 360 - 240
==> 2y = 120
==> y = 60
Thus the cost of a room per day is $80 and that for a car is $60