Question 1205729

let  adult passengers be {{{x}}} and child passengers {{{y}}}

if a cruise ship had 3 times as many adult passengers as child passengers when it left its first port, we have

{{{x=3y}}}....eg.1

if at a new port, {{{116}}} adults and {{{50}}} children boarded the ship, we have

{{{(x+116)+(y+50)}}}

if there are now {{{1216}}} more adults than children on the ship, we have

{{{(x+116)=(y+50)+1216}}}

{{{x=y+50+1216-116}}}

{{{x=y+1150}}}.....eq.2


substitute {{{x}}} from eq.1


{{{3y=y+1150}}}.....eq.2, solve for{{{ y}}}

{{{3y-y=1150}}}

{{{2y=1150}}}

{{{y=1150/2}}}

{{{y=575}}}

go to

{{{x=3y}}}....eg.1, substitute {{{y}}}

{{{x=3*575}}}

{{{x=1725}}}


How many children were on the ship at first?

{{{575}}}