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$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?

Respuesta :

JeanaShupp

Answer: 68 adults and 51 students attended the play.

Step-by-step explanation:

Let x = Number of adults

y= Number of students

As per given,

[tex]10x+6y=986\ \ \ \ (i)\\\\ y=\dfrac34x\ \ \ \ (ii)[/tex]

Put (ii) in (i) , we get

[tex]10x+6(\dfrac34x)=986\\\\\Rightarrow\ 10x+\dfrac{9}{2}x=986\\\\\Rightarrow\dfrac{29}{2}x=986\\\\\Rightarrow\ x=\dfrac{986\times2}{29}\\\\\Rightarrow\ x=68[/tex]

So, [tex]y=\dfrac{3}{4}\times68=51[/tex]   (from (ii))

Hence, 68 adults and 51 students attended the play.

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