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?

$50

$75

$150

$200

Answer 1

let the hotel cost = $ x per day and
let the cost of amusement park = $ y per day
So for first plan 3x + 2y = 450 ------------ (I)
and for second plan 5x + 3y = 700 ------------ (II)

Multiply (I) by 5 and (II) by -3 and add the resulting equations

15x + 10y = 2250
-15x - 9y = -2100 we get

y = 150

So, the cost of 1 day trip to the amusement park is $ 150