Question

30 points

The school that Jessica goes to is selling tickets to a fall musical. On the first day of ticket sales
the school sold 6 senior citizen tickets and 5 student tickets for a total of $50. The school took in
$44 on the second day by selling 8 senior citizen tickets and 1 student ticket. Find the price of a
senior citizen ticket and the price of a student ticket.
6C+ SS=50
8C+15=44

Answer 1

The price of a senior citizen ticket to the fall musical is $6

The price of a student citizen ticket to the fall musical is $4

Explanation:

C = the price of a senior citizen ticket to the fall musical

S = the price of a student citizen ticket to the fall musical

Day 1:

6C + 5S = 50

Day 2:

8C + 1S = 44

Manipulate the equations so that they have a common coefficient.

Multiple Day 2's equation by 5.

8C + 1S = 44

40C + 5S = 220

Subtract Day 2's equation from Day 1's

(40C + 5S = 220) - (6C + 5S = 50)

(40C + 5S) - (6C + 5S) = 220 - 50

(40C - 6C) + (5S - 5S) = 220 - 50

34C = 170

C = 5

Substitute C into either equation to solve for S.

Day 1:

6C + 5S = 50

6(5) + 5S = 50

30 + 5S = 50

5S = 50 - 30

5S = 20

S = 4

Day 2:

8C + 1S = 44

8(5) + 1S = 44

40 + 1S = 44

1S = 44 - 40

S = 4