Question

I need some help on this word problem please do it for me (12)

Answer 1

The first thing we need to do is identify the important values, our variables, and our equations that model or describe our problem.

• A total of 560 tickets were sold.

• Tickets can be ,A,dult or ,S,tudent

`A+S=560\to(1)`

• The total of tickets sold $3166

,

• The value of the Adult ticket is $8

,

• The value of the Student ticket is $3.5

`8A+3.5S=3166\to(2)`

We can see that A and S correspond to the number of Adult or Student tickets sold. We solve the equations to find our numbers.

`A=560-S\to\text{(1)}`
`\begin{gathered} 8(560-S)+3.5S=3166 \\ 8*560-8S+3.5S=3166 \\ S(3.5-8)=3166-4480 \\ -4.5S=-1314 \\ S=(-1314)/(-4.5) \\ S=292 \end{gathered}`
`\begin{gathered} A=560-292 \\ A=268 \end{gathered}`

In total, 292 Student tickets and 268 Adult tickets were sold.