Algebra Question

Question

Solve the system of equations. Show all work. Jill's school is selling tickets to a spring musical. On the first day of ticket sales, the school sold 7 senior citizen tickets and 9 child tickets for $64. The school took in $92 on the second day by selling 11 senior citizen tickets and 12 child tickets. What is the price of a senior citizen ticket and one child ticket?

Answer 1

Let's use the variable, s, represent the price of a senior ticket and the variable, c, represent the price of a child ticket.

We can write the follwoing equations to represent the two days sales amounts:

7s + 9c = $64

11s + 12c = 92

Now we can solve these two equations with two unknowns to find the price of eacj type of ticket.

Multiply the first equation by -11 and the secong equation by 7 to find the proce of the child ticket first:

7s + 9c = $64 becomes -77s - 99c = -704

11s + 12c = 92 becomes 77s + 84c = 644

Now combine these two "new" equations:

-77s - 99c = -704

77s + 84c = 644

-15c = -60

c = $4

The cost of one child ticket is $4.

Now substitute $4 for c in either of the original equations to find the price s of one senior. (Let's use the first equation.)

7s + 9c = 64

7s + 9 • 4 = 64

7s + 36 = 64

7s + 36 - 36 = 64 - 36

7s = 28

s = $4

The price of a senior ticket is $4 also.