Four adults and three children go to a theatre for $74, whereas two adults and five children are charged $58. Find the price of an adult’s ticket and a child’s ticket.

adult’s ticket = $14   ||     child’s ticket = $6

Step-by-step explanation:

Let adults ticket cost be a , children's ticket cost be c

4a + 3c = $74 from theory 1

2a + 5c = $58 from theory 2

Making a the subject for both:

4a + 3c = $74

4a = 74 - 3c

a = ( 74 - 3c )/4 equation 1

2a + 5c = $58

2a = 58 - 5c

a = ( 58 - 5c )/2 equation 2

Solving simultaneously:

( 58 - 5c )/2 =  ( 74 - 3c )/4

4( 58 - 5c ) = 2( 74 - 3c )

232 - 20c = 148 -6c

232 -148 = -6c + 20c

84 = 14c

c = $6

Each children's ticket cost is $6

Then the adults ticket cost: ( 74 - 3c )/4

                                            : ( 74 - 3(6) )/4

                                            : $14