Question

A movie theater sold 125 tickets for a matinee. The total amount of money collected was $878 . Student tickets cost $7 , senior citizen tickets cost $6 , and general admission tickets cost $9 . There were 18 more student tickets sold than twice the amount of general admission tickets. Use the information in the problem to create a system of three linear equations in three variables, for the number of student tickets, for the number of senior citizen tickets and for the number of general admission tickets. Then use substitution to determine how many of each type of ticket was sold. Express the solution as an ordered triple, (,,) .

Answer 1

Answer: The Number of student tickets, senior citizen ticket and general admission tickets are 62, 41 and 22 respectively. It is expressed as (62,41,22).

Step-by-step explanation:

Let the Number of student tickets, senior citizen ticket and general admission tickets are x, y and z respectively.

It is given that the movie theater sold 125 tickets for a matinee. The total amount of money collected was $878 . Student tickets cost $7 , senior citizen tickets cost $6 , and general admission tickets cost $9 .

`x+y+z=125` ...... (1)

`7x+6y+9z=878` .... (2)

There were 18 more student tickets sold than twice the amount of general admission tickets.

`x=2z+18` ....(3)

Put
`x=2z+18` in equation (1) and (2).

The equation (1) will become,

`y+3z=107` .....(4)

The equation (2) will become,

`6y+23z=752` .....(5)

Solve equation (4) and (5) by elimination method we get,

`y=41,z=22`

Since
`z=22`, therefore
`x=62`.

Thus, the Number of student tickets, senior citizen ticket and general admission tickets are 62, 41 and 22 respectively. It is expressed as (62,41,22).