Question 1179222


At a local Brownsville play production, {{{420}}} tickets were sold. 

let's ticket that cost ${{{8}}} be {{{a}}}, ticket that cost ${{{10}}} be {{{b}}}, and ticket that cost ${{{12}}} be {{{c}}}


{{{a+b+c=420}}}.........eq.1


if the total income from ticket sales reached ${{{3920}}}, we have

{{{8a+10b+12c=3920}}}.....eq.2

If the combined number of ${{{8}}} and ${{{10}}} priced tickets sold was 5 times the number of ${{{12 }}}tickets, we have
 

{{{a+b=5c}}}....eq.3


go to

{{{a+b+c=420}}}.........eq.1, substitute {{{a+b}}} from eq.3

{{{5c+c=420}}}

{{{6c=420}}}

{{{c=420/6}}}

{{{c=70}}}

go to

{{{a+b=5*70}}}....eq.3

{{{a+b=350}}}..........solve for {{{a}}}

{{{a=350-b}}}..............eq.1)


go to

{{{8a+10b+12c=3920}}}.....eq.2, substitute {{{a}}} and {{{c}}}

{{{8(350-b)+10b+12*70=3920}}}.......solve for {{{b}}}

{{{2800-8b+10b+840=3920}}}

{{{3640+2b=3920}}}

{{{2b=3920-3640}}}

{{{2b=280}}}

{{{b=140}}}


go to


{{{a=350-b}}}..............eq.1), substitute {{{b}}}

{{{a=350-140}}}

{{{a=210}}}


sold, how many tickets of each type were sold?

 {{{210}}} tickets that cost ${{{8}}} were sold, 
{{{140}}}tickets that cost ${{{10}}} were sold, 

and {{{70}}} tickets that cost ${{{12}}} were sold