Samantha is going on vacation for the summer and is trying to choose between two different plans. The first plan costs $450 for 3 days at a hotel and 2 days at an amusement park. The second plan offers 5 days at the same hotel and 3 days at the amusement park for $700. The cost of 1 day at the hotel and the amusement park is the same under both plans. How much does a 1 day trip to the amusement park cost?

Question

anonymous · Answer

I'm really stuck. these are my options $50
	$75
	$150
	$200

keana · Answer

Let h = cost of hotel per night and a = cost of amusement park for one day. Then we have two equations as follows:

$450 = 3h + 2a
$700 = 5h + 3a

multiply first eqn by 5 and second by -3

$2250 = 15h + 10 a
-$2100 = -15h - 9a

Now add them:

$150 = a

The cost of one day at the amusement park is $150.

anonymous · Answer

Let x = hotel expense
Let y = amusement park expense
3x + 2y = 450
5x + 3y = 700

-5(3x + 2y = 450)
3(5x + 3y = 700
-15x - 10y = -2250
15x + 9y = 2100
-y = -150
y = 150
The expense for 1 day at the amusement park is 150

anonymous · Answer

Thank you soooo much that that helped me understand it big time!

anonymous · Answer

You're welcome :)

anonymous · Answer

can you guys help me on this one as well. I would really appreciate it!
Solve 3x - 5y = 17
9x - 15y = -4
 	
	(-1, -4)
	(4, -1)
	No Solutions
	Infinitely Many Solutions

anonymous · Answer

3x - 5y = 17
9x - 15y = -4

-3(3x - 5y = 17)
9x - 15y = -4

-9x + 15y = -51
9x - 15y = -4
0 = -55
Therefore, no solution. THese are parallel lines.

anonymous · Answer

Okay that is what I thought it was as well so thank you for helping me make sure. :)

anonymous · Answer

You're welcome. You know when it's infinitely many solutions right?