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There are 203 tickets sold for a college basketball game. Tickets were $4.50 for students and $9 for adults. The total amount collected was $1485. How many of each type of ticket were sold?

 Jan 22, 2020
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There are 203 tickets sold for a college basketball game.
Tickets were $4.50 for students and $9 for adults.
The total amount collected was $1485.


How many of each type of ticket were sold?

 

\(\text{Let tickets for students $= x$ } \\ \text{Let tickets for adults $= y$ } \)

 

\(\begin{array}{|rcll|} \hline \mathbf{x+y} &=& \mathbf{203~tickets} \\ y &=& 203 - x \\\\ \mathbf{$4.50x + $9y} &=& \mathbf{$1485} \\ 4.50x + 9(203 - x) &=& 1485 \\ 4.50x + 1827 - 9x &=& 1485 \\ -4.50x + 1827 &=& 1485 \\ -4.50x &=& 1485-1827 \\ -4.50x &=& -342 \quad | \quad *(-1) \\ 4.50x &=& 342 \quad | \quad :4.50 \\ \mathbf{x} &=& \mathbf{76~tickets} \\\\ y &=& 203 - x \\ y &=& 203 - 76 \\ \mathbf{y} &=& \mathbf{127~tickets} \\ \hline \end{array}\)

 

76 tickets for students
127 tickets for adults

 

laugh

 Jan 22, 2020

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