Question

Sarawong's school is selling tickets to the annual talent show. On the first day of ticket sales the
school sold 14 adult tickets and 14 child tickets for a total of $224. The school took in $44 on the
second day by selling 2 adult tickets and 6 child tickets. Find the price of an adult ticket and the
price of a child ticket.

Answer 1

Answer:

Price of the adult ticket is $13

Price of the child ticket is $3

Step-by-step explanation:

Lets x be the adult ticket and y be the child ticket.

Given:

School sold 14 adult tickets and 14 child tickets for a total of $224, so the first equation is.

$14x+14y=224$-------------(1)

And the school took in $44 on the  second day by selling 2 adult tickets and 6 child tickets, so the second equation is.

$2x+6y=44$---------------(2)

We find the price of an adult ticket and the  price of a child ticket by solving above system of equation.

Now, equation 2 multiplied by 7.

$7(2x+6y=44)$

$14x+42y=308$---------(3)

Now, equation 1 subtracted by equation 3.

$14x+42y=308$

$14x+14y=224$

-______________

14x is cancelled in both equations, so we get the equation.

$28y=84$

$y=\frac{84}{28}$

y = 3

Now, we substitute y = 3 in equation 2.

$2x+6(3)=44$

$2x+18=44$

$2x=44-18$

$2x=26$

$x=\frac{26}{2}$

x = 13

Therefore, the price of the adult ticket is $13 and the price of the child ticket is $3.