Question 1152162

let the number of adult plates be {{{x}}} and the number of child plates {{{y}}}

the Math Club raised ${{{277.50}}}.

child plates were sold for ${{{2.25}}} : {{{2.25y}}}
adult plates were sold for ${{{4.75}}} : {{{4.75x}}}

=>{{{4.75x+2.25y=277.50}}}.........eq.1

If there were {{{twice}}} as many child plates sold than adult plates,we have

{{{y=2x}}}.......eq.2...substitute in eq.1


{{{4.75x+2.25*2x=277.50}}}.........solve for {{{x}}}

{{{4.75x+4.50x=277.50}}}

{{{9.25x=277.50}}}

{{{x=277.50/9.25}}}

{{{x=30}}}

go to eq.2

{{{y=2x}}}..........substitute {{{x}}}

{{{y=2*30}}}

{{{y=60}}}



how many adult plates were sold?

answer: {{{x=30}}}

how many child plates were sold?

answer: {{{x=60}}}


check:

{{{4.75x+2.25y=277.50}}}

{{{4.75*30+2.25*60=277.50}}}

{{{142.5+135=277.50}}}

{{{277.50=277.50}}}