A movie theater charges $8.50 per child and $14 per adult. One evening the theater sells 201 tickets for a total of $2550. How many adult tickets were sold?

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Answer 1 · 2017-06-16T00:44:16

153 Adult tickets
48 Child tickets

Begin by assigning variables for the number of adult and child tickets sold.

#x =# number of adult tickets
#y =3 number of child tickets

Therefore, #x + y = 201#

Now
#14x =# sales of adult tickets
#8.50y =# sale of child tickets

Therefore, #14x + 8.50y = 2550#

Now we can set up an algebraic system and solve by substitution.

#x + y = 201#
#14x + 8.50y = 2550#

Begin by isolating the variable in the first equation

#x = 201 - y#

Substitute for #x# in the second equation

#14(201-y) + 8.5y = 2550#

#2814 -14y +8.5y = 2550#

#2814 - 2814 -5.5y = 2550 - 2814#

#-5.5y = -264#

#(-5.5y)/-5.5 = -264/-5.5#

#y = 48# child tickets

#x = 201 - 48#

#x = 153# adult tickets