Question

Two groups of people went to see Avatar in IMAX 3D. The first group spent $73.50 on two adult and
threechildren tickets. The othergroup spent $109.50 on five adult and two children tickets. What is
the cost for each type of ticket?

Answer 1

Sorry, but my english is not so good, but i hope you understandme:

2x + 3y = 73.5               ec. 1
5x + 2y = 109.5             ec. 2


if the ec. 2 is multipl by -1.5:
-7.5x - 3y = -164.25      ec. 3

The sum of ec. 1 and ec. 3:

2x  + 3y =  73.5
-7.5x -3y = -164.25

-5.5x = -90.75
x = -90.75/5.5
x = 16.5

The cost for adult is $16.50

Then, on the ec. 1:

2x + 3y = 73.5
2*16.5 + 3y = 73.5
33 + 3y = 73.5
3y = 73.5 - 33
3y = 40.5
y = 40.5/3

y = 13.5

The cost for Children is $13.5 each.

Check it out on ec. 2:

5x + 2y = 109.5

5*16.5 + 2*13.5 = 109.5
82.5 + 27 = 109.5

109.5 ≡ 109.5


Regards...