Algebra Context

Question

A group of friends wants to go to the amusement park. They have no more than $110 to spend on parking and admission. Parking is $19.25, and tickets cost $30.25 per person, including tax. Write and solve an inequality which can be used to determine x, the number of people who can go to the amusement park

Answer 1

The first thing that we want to look at is that they have no more than $110, so we want our total cost to be less or equal to than 110, giving us the right hand side of the equation as " ≤110". Parking is a flat fee of $19.25 regardless of the number of people attending, then the cost of the tickets will be the cost of one ticket, $30.25, multiplied by the number of people. This given us the left hand side of the equation "19.25 + n30.25", where n is the number of people. Putting together the left and right hand side, we obtain

19.25+n30.25≤110

The next part is to solve for n, which we do by first subtracting 19.25 from both sides, then dividing both sides by 30.25:

n ≤ (110-19.25)/30.25

n ≤ 3

So, the maximum amount of people who can go to the theme park is 3.