Question 1083064
given:
 Total amount paid is ${{{4642.00}}}
 tickets for {{{5}}} adults and {{{1}}} youth : 

let's tickets for adults be {{{x}}}  and for youth {{{y}}}

since youth ticket price is discounted {{{20}}}%={{{20/100=0.20}}} off the adult ticket price, we know that {{{x- 0.20x=y}}}

{{{ 0.80x=y}}}

so 
{{{5x + 0.80x = 4642 }}}

 {{{5.80x = 4642 }}}

{{{ x = 4642 /5.80}}}

{{{x=800.3448275862069}}}

{{{x=800.34}}}

ticket for adults cost {{{800.34}}}

{{{0.20*800.34=160.06}}}->  discount of {{{20}}}%

{{{800.34-160.06=640.28}}}->cost of the ticket for youth 

check:

{{{5*800.34+640.28=4001.7+640.28=4641.98=4642}}}