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 costs 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 costs.

Answer 1

Pretend the cost of the hotel is called "x" and the amusement park is "y"
make the equations.
450=3x+2y  and  700=5x+3y
since you're solving for amusement park, you basically just solve for y
multiply the first equation by 5 and the second equation by 3.
2250=15x+10y  and  2100=15x+9y
these are a system of equations so subtract one from the other to cancel the x values away.
150=y   so the answer is that a day trip to the amusement park costs $150