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A school is selling tickets to their annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets and 5 student tickets for a total of $102. On the second day, the school sold 7 senior citizen tickets and 5 student tickets for a total of $126. What did the school charge for one senior citizen ticket?

Respuesta :

Ammimochi

Let's mark or variables as c = senior Citizen and S = Student.


We know that:

4c + 5s = 102


7c + 5s = 126

Elimination seems to be an easy way to solve this. So, we multiply the first equation by -1, thus eliminate the student tickets for now:


-4c - 5s = -102


7c + 5s =  126


--------------------


3c = 24


Divide both sides by 3:


c = 8

Now we can solve for c and check our work:


4 * 8 + 5s = 102


32 + 5s = 102


5s = 70


s = 14



7 * 8 + 14 * 5 = 126


56 + 70 = 126


126 = 126


So senior citizen tickets are $8 and student tickets are $14.

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