Samantha is going on a 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$. The cost of 1 day at the hotel and the amusement park is the same under both plans. How much does a 1 day trip to the amusement park cost? ((I think it's 50$)) ??

Answer 1

hotel costs $h/day
park costs $p/day

3h + 2p = 450
5h + 3p = 700

15h + 10p = 2250
15h + 9p = 2100
subtract:
p = 150
so, h=50

3(50)+2(150) = 150 + 300 = 450
5(50)+3(150) = 250 + 450 = 700

SO, it looks like you solved the problem, but got the hotel and park switched.