Question

40 adults and 26 kids went to see a movie on the opening screening and revenues for the showing was $486.70. The next showing 20 adults and 31 kids went to see the same movie and the revenue was $332.45. How much was an adult ticket and how much was a kid ticket?

Answer 1

Adults = 40

Kids = 26

revenue = $486.70

40A + 26 K = 486.70

Adults= 20

Kids = 31

revenue = $332.45

20A + 31K= 332.45

Where :

A = price of an adult ticket

K= price of a kid ticket

We have the system of equations:

40A + 26 K = 486.70 (1)

20A + 31K= 332.45 (2)

Multiply (2) by 2 and subtract (2) to (1)

40A + 26 K = 486.70

-

40A + 62K = 664.9

_____________

-36K= -178.2

K= -178.2/-36

K= 4.95

Replace K on (1) and solve for A

40A + 26 K = 486.70

40A + 26 (4.95)= 486.70

40A +128.7 = 486.70

40A = 486.70 -128.7

40A= 358

A= 358/40

A= 8.95

Answer:

Adult ticket = $8.95

Kid ticket = $4.95