Molly school is selling tickets to the fall musical. on the first day of the ticket sales the school sold 13 adults tickets and 14 child tickets for the total of $351. The school took in $117 on the second day by selling 2 adult tickets and 7 child tickets. What is the price of each of one adult ticket and one child ticket?

Adult Ticket Price = $13

Child Ticket Price = $13

Step-by-step explanation:

Let price of adult ticket be "a" and child ticket be "c"

13 adult and 14 child equals $351, so we can write:

13a + 14c = 351

and

2 adult and 7 child equals $117, thus we can write:

2a + 7c = 117

We multiply 2nd equation by (-2) to get:

-2 * [2a + 7c = 117]

= -4a -14c = -234

Adding botht he "bold" equations, we get:

13a + 14c = 351

-4a -14c = -234

9a = 117

a = 117/9 = 13

Now to find b, we use the value of a gotten in the first equation:

13a + 14c = 351

13(13) + 14c = 351

169 + 14c = 351

14c = 182

c = 182/14 = 13

Hence,

Adult Ticket Price = $13

Child Ticket Price = $13

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32