Question

Can someone
help me solve this word problem will give 25 points.

Answer 1

S = price of a senior's ticket

C = price of a child's ticket

`\stackrel{ \textit{\LARGE 1st day} }{\stackrel{ \textit{9 seniors} }{9S}~~ + ~~\stackrel{ \textit{3 children} }{3C}~~ = ~~\stackrel{ \textit{total \$} }{96}} \\\\\\ \stackrel{ \textit{\LARGE 2nd day} }{\stackrel{ \textit{2 seniors} }{2S}~~ + ~~\stackrel{ \textit{9 children} }{9C}~~ = ~~\stackrel{ \textit{total \$} }{63}} \\\\[-0.35em] ~\dotfill`

`\stackrel{\textit{using the 1st equation}}{9S+3C=96}\implies 3C=96-9S\implies C=\cfrac{96-9S}{3}\implies C=32-3S \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{2S+9C=63}\implies 2S+9(32-3S)=63 \\\\\\ 2S+288-27S=63\implies 288-25S=63\implies 125-25S=0 \\\\\\ 125=25S\implies \cfrac{125}{25}=S\implies \boxed{5=S}\hspace{5em}\stackrel{ 32~~ - ~~3(5) }{\boxed{C=17}}`