Question

our schools art teacher took the class to a concert hall and paid $512 for 10 adult tickets and 9 childrens tickets. the next day, our music teacher took our class to the same concert hall and paid a total of $831 for 17 children and 15 adults. if ( a ) represents the price of an adult ticket, and ( c ) represents the price of a child’s ticket, which system of equations can be used to find how much each child ticket and each adult ticket cost?
a ( \begin{cases} 10a + 9c = 512 \\ 15a + 17c = 831 end{cases} )
b ( \begin{cases} 10c + 9a = 512 \\ 15c + 17a = 831 end{cases} )
c ( \begin{cases} 19(a + c) = 512 \\ 32(a + c) = 831 end{cases} )
d ( \begin{cases} 19ac = 512 \\ 32ac = 831 end{cases} )

Explanation:

Step1: Analyze first scenario

The art teacher bought 10 adult tickets (cost \(10a\)) and 9 children's tickets (cost \(9c\)) and paid $512. So the equation is \(10a + 9c = 512\).

Step2: Analyze second scenario

The music teacher bought 15 adult tickets (cost \(15a\)) and 17 children's tickets (cost \(17c\)) and paid $831. So the equation is \(15a + 17c = 831\).

Step3: Match with options

Option A has the two equations \(10a + 9c = 512\) and \(15a + 17c = 831\), which match our derived equations.

Answer:

A. \(10a + 9c = 512\)
\(15a + 17c = 831\)