Question

A theme park charges $20 for adults and $10 for children. One day the theme park sold 600 tickets and collected $9,600 in revenue. Let x represent the number of adult tickets sold and y represent the number of child tickets sold.

a) Setup the system of equations representing the above situation.

b) Express the system of equations in matrix form AX=B.

c) Using Cramer's Rule on the system of equations, determine how many tickets of each type were sold. Show all work/calculations as if you do not have a calculator. You will not receive full credit if any other method is used to solve the system.

d) How many of each type of ticket were sold on the day in question? Provide your answer using a complete sentence with appropriate units.

Answer 1

a. X + Y = 600

20X + 10Y = 9600

b. 1 1 X = 600

b. 20 10 Y 9600

c. X = 360 and Y = 240

d. 360 types of tickets were sold to adult and 240 types of ticket were sold to child.

Explanation:

A step by step solution to the problem is attached as an image.

Answer 2

Answer: 360 adults and 240 children tickets were sold.

Explanation:

a)

Let x represent the number of adult tickets sold and y represent the number of child tickets sold.

The theme park sold 600 tickets. It means that

x + y = 600

The theme park charges $20 for adults and $10 for children. They collected $9,600 in revenue. It means that

20x + 10y = 9600

b) the matrix form of Ax = B is

1 1 x1 600

20 10 x2 9600

c)

Determinant, D = (1 × 10) - (20 × 1) =

- 10

Dx(replacing the first column) is

(600 × 10) - (9600 × 1) = - 3600

x = Dx/D = - 3600/- 10 = 360

Dy(replacing the second column) is

(9600 × 1) - (600 × 20) = - 2400

y = Dy/D = - 2400/- 10 = 240