Question

At a movie theater, the price of 4 adult tickets and 3 child tickets is $65. The price of 9 adult tickets and 6 child tickets is $141. Write and solve a system of equations to find the price of an adult ticket and the price of a child ticket.

Answer 1

price of adult ticket = $11

price of child ticket = $7

Explanation:

Let x = price of adult ticket

y = price of child ticket

4x+3y=65. eq. 1

9x+6y=141. eq.2

solving for eqs. 1&2

x=11

y=7

Answer 2

$7 Child Tickets $11 Adult Tickets

Explanation:

x=adult tickets

y=child tickets

4x+3y=65

9x+6y=141

multiply the entire top equation by 2 making it

8x+6y=130 and the bottom stays the same so it would be

9x+6y=141 then you multiply one of the equations (mine will be the top one) by -1

so itll turn out to be

-8x-6y=-130

9x+6y=141

y cancels out and 9-8 is 1 so you are left with x

x=11 (adult tickets)

you plug the 11 into any x (mine will be in the top equation) and you substitute

4(11)+3y=65

44+3y=65

65-44=21

3y=21

3y/3=21/3

y=7(child tickets)