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?

Answer 1

Define h=cost of hotel per day
a=cost of amusement park per day

Then set-up and solve the system:
3h+2a=450 [1]
5h+3a=700 [2]

Mutliply [1] by 3 and mult [2] by -2, and make a linear combination to eliminate the a-variables:
9h+6a=1350 [1]'
-10h-6a=-1400 [2]'
===========
-h =-50
h=50

Now sub h=50 into either given equation to find a; i choose [1];
3(50)+2a=450
2a=300
a=150

So, the cost of the hotel is $50 per day, and the cost of the amusement park is $150 per day.