Question 1149429
At a high school baseball game, G.O. members paid $3.50 each and non-members paid $5.00 each. There were 20 more G.O. members at the game than non-members. If the total receipts was $750, how many tickets of each kind were sold?

let G.O. members tickets be {{{x}}} and non-members tickets   {{{y}}}

given:
G.O. members paid ${{{3.50}}} each =>{{{3.50x}}}

non-members paid ${{{5.00}}} each=>{{{5.00y}}}

if the total receipts was ${{{750}}}, we have

{{{3.50x+5.00y=750}}}.......eq.1

if there were {{{20}}} more G.O. members at the game than non-members, we have

{{{x=y+20}}}........eq.2-> substitute in eq.1

{{{3.50(y+20)+5.00y=750}}}.......eq.1....solve for {{{y}}}

{{{3.50y+70+5.00y=750}}}

{{{8.50y=750-70}}}

{{{8.50y=680}}}

{{{y=680/8.50}}}

{{{y=80}}}->the number of non-members tickets 

then

{{{x=y+20}}}........eq.2
{{{x=80+20}}}
{{{x=100}}}->the number of G.O. members tickets 

check:

 {{{3.50x+5.00y=750}}}.......eq.1
{{{3.50*100+5.00*80=750}}}
{{{350+400=750}}}
{{{750=750}}}