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?

From all the information given, you're going to have to create two equations and solve accordingly. 

If x=cost for one day at hotel; and y=cost for one day at amusement park then,

eq1 : 450=3x+2y ; eq2: 700=5x+3y

The total cost of the trip will be number of days spent at each location multiplied by the cost.

If you multiply equation 1 by 3 and equation 2 by 2 and subtract equation 2 from 1, than you will be able to isolate x.

1400=10x+6y
1350=9x+6y

x=$50; then plug back into any equation to find y.

450=3*50 + 2y

y=$150