#### Answer

An adult ticket's is 29 dollars.
A child ticket's is 18 dollars.

#### Work Step by Step

Let $a$ be the price of an adult's ticket.
Let $c$ be the price of a child's ticket.
Three adults and four children must pay 159 dollars.
$3a+4c=159$
Two adults and three children must pay 112 dollars.
$2a+3c=112$
$3a+4c=159$
$2a+3c=112$
Multiply first equation by 2 and second equation by -3.
$6a+8c=318$
$-6a-9c=-336$
Add both equations.
$-c=-18$
$c=18$
Solve for $a$
$2a+3c=112$
$2a+3(18)=112$
$2a+54=112$
$2a=58$
$a=29$
An adult's ticket is 29 dollars.
A child's ticket is 18 dollars.