Question

The Stump family went to the pumpkin patch and bought 1 adult ticket and 2 child tickets for 10 dollars. The Smith family went to the same pumpkin patch and purchased 3 adult tickets and 3 child tickets for 24 dollars. Their purchases can be modeled by the equations a+2c=10
and 3a+3c=24
, respectively, where a represents the price of an adult’s ticket and c represents the price of a child’s ticket. Graph each of the linear functions and find the price of a child’s ticket.(1 point)
Responses

The cost of a child’s ticket is $4.00.
The cost of a child’s ticket is $4.00. - no response given

The cost of a child’s ticket is $2.00.

Answer 1

Solve the system:
a + 2c = 10 -> a = 10 − 2c
Substitute into 3a + 3c = 24:
3(10 − 2c) + 3c = 24
30 − 6c + 3c = 24
−3c = −6 => c = 2

So a child’s ticket costs $2. (The two lines intersect at (a,c) = (6,2).)