Question 1155419


A play was attended by{{{ 320}}} people. 

Regular tickets {{{x}}} were ${{{15}}} each, while student tickets {{{y}}} were priced at ${{{10}}}. 

total number of tickets:

{{{x+y=320}}}.....eq.1

The total receipts were ${{{4200}}}. 

${{{15x+10y=4200}}}.......eq.2

Set up a system of linear equations in order to determine how many of each types of tickets were sold.

{{{x+y=320}}}.....eq.1......both sides multiply by {{{15}}}
{{{15x+10y=4200}}}.......eq.2
------------------------------------------

{{{15x+15y=4800}}}.....eq.1
{{{15x+10y=4200}}}.......eq.2
------------------------------------------subtract eq.2 from eq.1

{{{15x+15y-(15x+10y)=4800-4200}}}

{{{15x+15y-15x-10y=600}}}

{{{15y-10y=600}}}

{{{5y=600}}}

{{{y=600/5}}}

{{{y=120}}}

go to

{{{x+y=320}}}.....eq.1, substitute {{{y}}}

{{{x+120=320}}}

{{{x=320-120}}}

{{{x=200}}}

 {{{200}}} of regular tickets and   {{{120}}} of student tickets were sold