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Tickets at a particular movie theater have different rates for adults and children. On Friday, the theater sold 4 adult tickets and 7 child tickets for $83. The next day, the theater sold 5 adult tickets and 6 children tickets for $90. What is the price for the adult ticket and the price for the child ticket?

Respuesta :

Answer: The price for the adult tickets is $12 and the price for the child ticket is $5.

Step-by-step explanation:

Let the price for the adult ticket be x

Let the price for the child ticket be y

According to question, On Friday ,

[tex]4x+7y=83[/tex]

and on next day,

[tex]5x+6y=90[/tex]

Now, we will use "Substitution Method" to solve the system of equations :

[tex]5x+6y=90\\\\5x=90-6y\\\\x=\frac{90-6y}{5}[/tex]

so, we will put the value of x in the first equation i.e.

[tex]4x+7y=83\\\\4(\frac{90-6y}{5})+7y=83\\\\360-24y+35y=83\times 5\\\\35y-24y=415-360\\\\11y=55\\\\y=\frac{55}{11}\\\\y=5[/tex]

Now, put the value of y in the equation that is given by

[tex]x=\frac{90-6y}{5}\\\\x=\frac{90-6\times 5}{5}\\\\x=\frac{90-30}{5}\\\\x=\frac{60}{5}\\\\x=\$12[/tex]

Hence, the price for the adult tickets is $12 and the price for the child ticket is $5.


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