Question 708630

let an adult ticket  be {{{x}}} and a child’s ticket {{{y}}}

A local movie theater charges ${{{12}}} for an adult ticket and 
${{{10}}} for a child’s ticket. 

A group of {{{eight}}} people (adult and children) 

{{{x+y=8}}}................eq.1
spent a total of ${{{86}}}
{{{12x+10y=86}}}........eq.2
on tickets to a movie. 

How many adults and how many children were in the group?

solve the system:
{{{x+y=8}}}................eq.1....both sides multiply by {{{10}}}
{{{12x+10y=86}}}........eq.2
_________________________with the elimination method


 {{{10x+10y=80}}}................eq.1
-
{{{12x+10y=86}}}........eq.2.subtract eq.2 from eq.1
_________________________

{{{10x+10y-12x-10y=80-86}}}

{{{10x+cross(10y)-12x-cross(10y)=-6}}}

{{{-2x=-6}}}....both sides multiply by {{{-1}}}

{{{2x=6}}}

{{{x=6/2}}}

{{{highlight(x=3)}}}.....# of adults in the group

now go back to eq. 1 and find {{{y}}}

{{{3+y=8}}}................eq.1

{{{y=8-3}}}

{{{highlight(y=5)}}}......# of children in the group