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The drama club sold 1500 tickets for the end-of-year performance. Admission prices were $12 for adults and $6 for students. The total amount collected at the box office was $15,480. How many students attended the play?

chitsuii  Jul 3, 2018
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The drama club sold 1500 tickets for the end-of-year performance.
Admission prices were $12 for adults and $6 for students.
The total amount collected at the box office was $15,480.
How many students attended the play?

 

Let a = adults

Let s = students

 

\(\begin{array}{|lrcll|} \hline (1) & a + s &=& 1500 \\ & a &=& 1500 -s \\\\ (2) & 12 a + 6 s &=& 15480 \quad & | \quad : 12 \\ & a + \dfrac{s}{2} &=& 1290 \\ & a &=& 1290 - \dfrac{s}{2} \\\\ \hline (1) = (2): & a = 1290 - \dfrac{s}{2} &=& 1500 -s \\ & 1290 - \dfrac{s}{2} &=& 1500 -s \quad & | \quad + s \\ & 1290 +s - \dfrac{s}{2} &=& 1500 \quad & | \quad -1290 \\ & s - \dfrac{s}{2} &=& 1500 -1290 \\ & \dfrac{s}{2} &=& 210 \quad & | \quad * 2 \\ & \mathbf{ s} & \mathbf{=}& \mathbf{420} \\\\ & a &=& 1500 -s \\ & a &=& 1500 - 420 \\ & \mathbf{ a} & \mathbf{=}& \mathbf{ 1080 } \\ \hline \end{array}\)

 

420 students attended the play.

 

laugh

heureka  Jul 3, 2018

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