If three adults and two children go to the movies, it costs $33.50. if one adult and four children go to the movies, it costs $30.50. what is the cost of one adult movie ticket?

$5.80
$6.40
$7.30

1st equation: 3a +2c =33.50

2nd equation: 1a + 4c = 30.50

multiply 2nd equation by 3 so the a's equal the first equation

1a +4c = 30.50 x 3 = 3a +12c = 91.50 (3rd equation)

subtract 1st equation from 3rd equation:

3a +12c =91.50 - 3a + 2c = 33.50 = 10c = 58

c=58/10 = 5.80

 children's ticket cost 5.80

 now substitute that into the 1st equation and solve for a

3a +2c =33.50 =

3a +2(5.80) = 33.50

3a +11.60 =33.50

3a = 21.90

a = 21.90/3 = 7.30

 adult tickets cost $7.30

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