Question

our schools art teacher took his 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 dollars for 17 children and 15 adults.
if $a$ represents the price of an adult ticket, and $c$ represents the price of a childs ticket, which system of equations can be used to find how much each child ticket and each adult ticket cost?
a. $19(a + c) = 512$
$32(a + c) = 831$
b. $10a + 9c = 512$
$15a + 17c = 831$
c. $19ac = 512$
$32ac = 831$
d. $10c + 9a = 512$
$15c + 17a = 831$

Explanation:

Step1: Set up first equation

Cost for 10 adults + 9 children = 512:
$10a + 9c = 512$

Step2: Set up second equation

Cost for 15 adults +17 children =831:
$15a + 17c = 831$

Step3: Match to options

The system matches option D.

Answer:

D. $10c + 9a = 512$; $15c + 17a = 831$