Question

A particular movie theater charges $7.00 per adult and $4.50 per child. Suppose 450 people attended a movie and the total revenue from ticket sales was $2650. Write linear equations for the two constraints, where z represents the number of adults attending the

movie and y represents the number of children attending the movie. 1= ,2=?

Answer 1

7z + 4.5y = 2650

z + y = 450

Explanation:

The first equation represents the amount of money made from ticket sales for both adult and child tickets.

The second equation represents the amount of customers, both adult and child, that attended the theatre.

Using both equations you cans find the number of adults and children that attended the theatre.

Cheers.

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Edit: Solving for the variables

There are two easy ways to solve for these values. The first is using an augmented matrix and solving with that method.

7 4.5 | 2650

1 1 | 450

After are augmented matrix is set up, we simply use row operations on the matrix to solve for 1s on the diagonal.

The second method for solving is equation addition or variable substitution to solve for each variable.

7z + 4.5y = 2650

z + y = 450

7(450-y) + 4.5y = 2650

3150 - 7y + 4.5y = 2650

-2.5y = -500

y = 200

Plug back in y into one of the equations to solve for z.

z + 200 = 450

z = 250

So there were 250 adults and 200 children.