Question

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?

Answer 1

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 ,

$4x+7y=83$

and on next day,

$5x+6y=90$

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

$5x+6y=90\\\\5x=90-6y\\\\x=\frac{90-6y}{5}$

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

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

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

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

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