Answer:
The price of one adult ticket is $11 and the price of one student ticket is $6.
Step-by-step explanation:
We can write a system of equations to represent the situation. Let a represent the price of adult tickets sold and s represent the price of student tickets.
On the first day, nine adult tickets and 12 student tickets were sold for a total of $171. Hence:
[tex]\displaystyle 9a + 12s = 171[/tex]
And on the second day, 13 adult tickets and 14 student tickets were sold for a total of $227. Hence:
[tex]\displaystyle 13a + 14s = 227[/tex]
This yields a system of equations:
[tex]\displaystyle \left\{ \begin{array}{l} 9a + 12s = 171 \\ 13a + 14s = 227\end{array}[/tex]
We can solve using elimination. Note that the LCM of 12 and 14 is 84. Hence, we can multiply the first equation by -7 and the second by 6:
[tex]\displaystyle \left\{ \begin{array}{l} -63a + 84s = -1197 \\ 78a + 84s = 1362\end{array}[/tex]
Adding the two equations together now produces:
[tex]\displaystyle \begin{aligned} (-63a + 84s) + (78a + 84s) &= (-1197) + (1362) \\ 15a &= 165 \\ a&=11\end{aligned}[/tex]
Therefore, the price of one adult ticket is $11.
To find the price of one student ticket, use either one of the original equations:
[tex]\displaystyle \begin{aligned} 9a + 12s &= 171 \\ 9(11) + 12s &= 171 \\ 99 + 12s &= 171 \\ 12s &= 72 \\ s &= 6 \end{aligned}[/tex]
In conclusion, the price of one adult ticket is $11 and the price of one student ticket is $6.
