Question 1151939




let adult tickets be {{{x}}}, child tickets {{{y}}}, and senior tickets {{{z}}}=>

{{{x+y+z=63}}}

if the ratio of adult to child tickets was {{{5:1}}}, we have

{{{x:y=5:1}}}
{{{x=5y}}}........eq.1

if the ratio of adult to senior tickets was {{{5:3}}}, we have

{{{x:z=5:3}}}
{{{3x=5z}}}
{{{x=5z/3}}}........eq.2

from eq.1 and eq.2 we have

{{{5y=5z/3}}}
{{{y=5z/(3*5)}}}
{{{y=z/3}}}..........eq.2a



if art museum sold {{{63}}} tickets, we have

{{{x+y+z=63}}}......substitute {{{x}}} from eq.2 and {{{y}}} from eq.2a

{{{5z/3+z/3+z=63}}}..........both sides multiply by {{{3}}} and solve for {{{z}}}

{{{5z+z+3z=63*3}}}

{{{9z=189}}}

{{{z=189/9}}}

{{{z=21}}}

go to {{{x=5z/3}}}........eq.2,substitute {{{z}}}

 {{{x=(5*21)/3}}}

 {{{x=5*7}}}

 {{{x=35}}}
 
{{{y=z/3}}}
{{{y=21/3}}}
{{{y=7}}}

answer: 
 {{{35}}} adult tickets were sold, 
{{{7}}} child tickets were sold
{{{21}}}  senior tickets  were sold