Question 971452
make 2 equations
one for the total amount of people and one for the amount of tickets sold


x=children
y=adults


{{{x+y=630}}}
there are 630 people total. you add the children and adults together to find the total.


{{{2x+5y=2910}}}
the total amount of ticket sales is the adult sales and the children sales combined. 
The sales of the children tickets is the $2 times the number of tickets.
The sales of the adult tickets is the $5 times the number of tickets.


{{{x+y=630}}} can be solved for y
{{{x-x+y=630-x}}}
{{{0+y=630-x}}}
{{{y=630-x}}}
This can be used to find x in the other problem.
{{{2x+5y=2910}}}
{{{2x+5(630-x)=2910}}}
{{{2x+(5*630)+(5*(-x))=2910}}}
{{{2x+3150-5x=2910}}}
{{{-3x+3150=2910}}}
{{{-3x+3150-3150=2910-3150}}}
{{{-3x=-240}}}
{{{(-3x)/(-3)=(-240)/(-3)}}}
{{{x=80}}}


80 childrens tickets were sold.


To find the number of adults tickets sold, plug 80 into the first equation
{{{x+y=630}}}
{{{80+y=630}}}
{{{y+80-80=630-80}}}
{{{y=550}}}

550 adult tickets were sold.


to check if this is correct plug it into the second equation


{{{2x+5y=2910}}}
{{{2(80)+5(550)=2910}}}
{{{160+2750=2910}}}
{{{2910=2910}}}


80 childrens tickets and 550 adults tickets were sold.


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