Question 1136833


If {{{119}}} adults ={{{x}}} and children= {{{y}}} attend a concert, we have 

{{{x+y=119}}}.....eq.1

and if tickets for adults cost ${{{4}}} while tickets for children cost ${{{3.25}}}, and total receipts for the concert was ${{{431.75}}}, we have 

{{{4x+3.25y=431.75}}}.....eq.2

solve this system:
{{{x+y=119}}}.....eq.1-> both sides multiply by {{{4}}}
{{{4x+3.25y=431.75}}}.....eq.2
------------------------------------------------

{{{4x+4y=476}}}.....eq.1 
{{{4x+3.25y=431.75}}}.....eq.2
------------------------------------------------subtract

{{{4x+4y-4x-3.25y=476-431.75}}} 

{{{4y-3.25y=476-431.75}}} 

{{{0.75y=44.25}}} 

{{{y=44.25/0.75}}}

{{{y=59}}}


go to eq.1, plug in {{{y}}} value

 
{{{x+y=119}}}.....eq.1

{{{x+59=119}}}

{{{x=119-59}}}

{{{x=60}}}


so, there was {{{60}}} adults and {{{59}}} children