Last tuesday, regal cinemas sold a total of 8500 movie tickets. proceeds totaled 64000. tickets can be bought in one of the 3 ways: a matinee admission costs $5, student admission is $6 all day, and regular admissions are $8.50. how many of each type of ticket was sold if twice as many students tickets were sold as matinee tickets?

Number of student ticket is $571

Number of matinee ticket is $1142

Number of regular ticket  is  $6,787

Step-by-step explanation:

Let number of student ticket be x

Let number of matinee ticket be 2x

Number of regular ticket be 8500 - (x + 2x)

                                              = 8500 - 3x

Total cost is:

$( 5x + ( 6 x 2x) + (8500 - 3x) x 8)

= $( 5x + 12x + 68000 + 24x)

= $( 68000 - 7x)

From the condition given

68000 - 7x = 64000

7x = 4000

x = 4000 / 7

x = 571.43

x = 571

Number of student ticket is $571

Number of matinee ticket is 2 x 571 = $1142

Number of regular ticket  = 8500 - (3 x 571)

                                              = 8500 - 1713

                                              = $6,787

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)