sat math that is really hard

Question

)The school that Nick goes to is selling tickets to their annual talent show. On the first day of ticket sales, they sold 12 adult tickets and 15 children tickets and made $132. On the second day of ticket sales, they sold 8 adult tickets and 11 children tickets for $92.

 

Determine the cost of each adult ticket and each children’s ticket.

 

Answer 1

Let “a” be the price of an adult ticket.

Let “c” be the price of a children ticket.

1st way:

12a + 15c = 132 (1)

8a + 11c = 92 (2)

Subract (2) from (1):

4a + 4c = 40

a + c = 10

a = 10 – c

120 – 12c + 15c = 132

3c = 12

c = 4

then a = 10 – 4 = 6

2nd way:

12a + 15c = 132 (1)

8a + 11c = 92 (2)

Divide (1) by “4”:

4a + 5c = 44 (3)

Rewrite (2) as

2(4a + 5c) + c = 92

c = 92 – 2 • 44 = 4

From (3):

4a = 44 – 5 • 4 = 24

a = 6