Question

Students and adults purchased tickets for a recent school play. All tickets were sold atthe ticket booth (discounts of any type) were not allowed.Student tickets cost $8 each, and adult tickets cost $10 each. A total of $1,760 wascollected. 200 tickets were sold.a. Write a system of equations that can model the number of student and adulttickets sold at the ticket booth for the play.

Answer 1

Given:

Cost of students tickets is, c (s) = $8.

Cost of adult tickets is, c (a) = $10.

Total cost collected for by selling the tickets is, c (t) = $1,760.

Number of tickets sold is, n = 200.

The objective is to find the system of equations that can model the number of students and adults tickets sold at the booth.

Consider the number of students as x and number of adults as y.

Then, the equation of total numner of students will be,

`\begin{gathered} \text{Number of students+Number of adults=n} \\ x+y=200\ldots\ldots\ldots..(1) \end{gathered}`

Now, the cost equation can be calculated as,

`\begin{gathered} c(s)\cdot x+c(a)\cdot y=c(t) \\ 8x+10y=1760\ldots\ldots..\ldots..(2) \end{gathered}`

Hence, the system of equations that can model the number of students and adults tickets are x + y = 200 and 8x + 10y = 1760,