Question

Mr. Accardi sold 600 tickets for the high school play. If adult tickets cost $6.00 each and student tickets cost $4.00 each, how many of each type of ticket did he sell if $2,900.00 was collected in ticket money?

Answer 1

Given:

Total number of tickets = 600

Cost of adult ticket = $6.00

Cost of student ticket = $4.00

Total sales = $2900.00

To find:

The number of tickets of each type.

Solution:

Let the number of adult tickets be x and number of student tickets be y.

According to the question,

$x+y=600$        ...(i)

$6x+4y=2900$      ...(ii)

Multiply equation (i) by 4 and subtract the result from (ii),

$6x+4y-4(x+y)=2900-4\times 600$

$6x+4y-4x-4y=2900-2400$

$2x=500$

Divide both sides of 2.

$x=250$

Put x=250 in (i).

$250+y=600$

$y=600-250$

$y=350$

Therefore, number of adult tickets is 250 and number of student tickets is 350.