Question

Is the total ticket sales was $2212, how many children, students, and adults attended?

Answer 1

Let the number of children attended be c;

Let the number of adults attended be a;

and let the number of students that attended be s;

Then;

`\begin{gathered} c+s+a=305\ldots\ldots\ldots\ldots\text{equation 1} \\ 5c+7s+12a=2212\ldots\ldots.equation\text{ 2} \end{gathered}`

But there are half as many adults as there are children, then;

`\begin{gathered} a=(1)/(2)c \\ c=2a\ldots\ldots\ldots\ldots\ldots\text{. equation 3} \end{gathered}`

By substituting equation 3 in equation 1 and equation 2, we have;

`\begin{gathered} 2a+s+a=305 \\ 3a+s=305\ldots\ldots\ldots\ldots\text{ equation 4} \\ 5(2a)+7s+12a=2212 \\ 22a+7s=2212\ldots\ldots\ldots\text{.}\mathrm{}\text{equation 5} \end{gathered}`

Solving equation 4 and equation 5 simultaneously, we have;

`\begin{gathered} \text{From equation 4;} \\ s=305-3a \\ \text{put s=305-3a in equation 5;} \\ 22a+7(305-3a)=2212 \\ a=2212-2135 \\ a=77 \\ \text{Put a=77 in s=305-3a;} \\ s=305-3(77) \\ s=74 \end{gathered}`

Then, we substitute the value of a and s in equation 1 to get the value of c;

`\begin{gathered} c+74+77=305 \\ c=154 \end{gathered}`

154 children attended

74 students attended

77 adults attended.