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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. What is the cost per day for the room and for the car?


Explain how you did it.

2006-11-05 03:40:16 · 2 answers · asked by xolifes2sh0rtox 1 in Education & Reference Other - Education

2 answers

This solution involves two unknown variables and uses a technique of eliminating one of the variables in order to isolate and solve for the other.

Assumptions:

x = price per day of a hotel room
y = price per day of a rental car

Our two packages can therefore be expressed as follows:

3x + 2y = 360

4x + 3y = 500

For our equations to remain true, whatever we do on the left, we must do on the right. We are going to eliminate the y variable by creating an equal term in each equation. To do this we must create equivalent equations that have matching y values. To do this we will multiply the first equation by 3 and the second by 2, creating a value of 6y in each equation:

3(3x + 2y) = 3 * 360

or

9x + 6y = 1080

to adjust equation #2

2(4x + 3y) = 2 * 500

or

8x + 6y = 1000

Now we will subtract the second equation from the first to isolate the x variable:

9x + 6y = 1080
-8x + 6y = 1000
_____________
1x + 0y = 80 or

x = 80

Once we know the value of x, we can solve for y by using the value of x. Now our original first equation becomes:

3x + 27y = 360 or

3 * 80 + 2y = 360 or

240 + 2y = 360, now substracting 240 from each side we get:

2y = 120, dividing each side by 2:

y = 60

We can check our answer on the second equation by substituting the values of x and y.

4 * 80 + 3 * 60 = 500 or

320 + 180 = 500 or

500 = 500

It checks.

2006-11-05 04:17:51 · answer #1 · answered by Magic One 6 · 0 0

i just answered that question.

and it was right.
wtf???

hello?

-3(3h+2c=360)
2(4h+3c=500)

-9h-6c=-1080
8h+6c=1000
therefore
h=80

then substitute.

3(80)+2c=360
-240 -240

2c=120

c=60

the car is 60$ a day and the hotel is 80$ a day.

2006-11-05 11:45:11 · answer #2 · answered by SuperstarKayluh 1 · 0 0

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