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?
A. $50
B. $75
C. $150
D.$200

Question

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?
A. $50
B. $75
C. $150
D.$200

anonymous · Answer

I'm terrible at word problems...

anonymous · Answer

x=1 day at the hotel
y=1 day at the amusement park
3x+2y=450

john_es · Answer

Ok, it goes well.

anonymous · Answer

5x+3y=700

john_es · Answer

Good job ;).

john_es · Answer

Now, time for the solution. ;)

anonymous · Answer

Where I have trouble haha

anonymous · Answer

The answer is C...? :)

john_es · Answer

Try reduction again. Multiplicate the first by -3 and the second by 2, then,
$$-9x-6y=-1350\
10x-6y=1400$$
Then sum both,
$$x=50$$
I left the rest to you (substitute in the first equation and you'll get it)
y=110

john_es · Answer

−9x−6y=−1350
10x+6y=1400
I mean

anonymous · Answer

I think I multiplied wrong...

anonymous · Answer

I either set it up wrong or messed up the multiplication

john_es · Answer

No, I missed up. The system is ok,
−9x−6y=−1350 
10x+6y=1400 
And you obtain x=50. Then, you'll have for the y, using 450=3x+2y,
450=150+2y
y=150.
Again you're right, it is C.

anonymous · Answer

Multiply the first equation by 5.
15x+10y=$2250
Multiply the second by -3
-15x-9y=-$2100
Next, I added them.
y=$150 :)