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Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $2,783 was collected on the sale of 1,235 tickets. How many of each type of ticket were sold?

 Jan 26, 2020
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Adult tickets to a basketball game cost $5.
Student tickets cost $1.
A total of $2,783 was collected on the sale of 1,235 tickets.
How many of each type of ticket were sold?

 

\(\text{Let number of adult tickets $=a$} \\ \text{Let number of student tickets $=s$}\)

 

\(\begin{array}{|rcll|} \hline a+s &=& 1235 \\ \mathbf{s} &=& \mathbf{1235-a} \\ \hline \end{array}\)

 

\(\begin{array}{|rcll|} \hline 5a+s &=& 2783 \\ 5a + (1235-a) &=& 2783 \\ 5a + 1235-a &=& 2783 \\ 4a + 1235 &=& 2783 \\ 4a &=& 2783-1235 \\ 4a &=& 1548 \quad | \quad : 4 \\ \mathbf{a} &=& \mathbf{387} \\\\ \mathbf{s} &=& \mathbf{1235-a} \\ s &=& 1235-387 \\ \mathbf{s} &=& \mathbf{848} \\ \hline \end{array}\)

 

The number of adult tickets is 387
The number of student tickets is 848

 

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 Jan 26, 2020

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