Question

$986 in revenue for a play. Tickets for the play cost $10 for adults and $6 for students. The number of students attending the play was LaTeX: \frac{3}{4}\:\:\: 3 4 the number of adults attending the play. How many adults and students attended the play?

Answer 1

Answer: 68 adults and 51 students attended the play.

Explanation:

Let x = Number of adults

y= Number of students

As per given,

`10x+6y=986\ \ \ \ (i)\\\\ y=\frac34x\ \ \ \ (ii)`

Put (ii) in (i) , we get

`10x+6(\frac34x)=986\\\\\Rightarrow\ 10x+(9)/(2)x=986\\\\\Rightarrow(29)/(2)x=986\\\\\Rightarrow\ x=(986*2)/(29)\\\\\Rightarrow\ x=68`

So,
`y=(3)/(4)*68=51` (from (ii))

Hence, 68 adults and 51 students attended the play.