the question is in the description, and its to find how much does a adult ticket cost vs student ticket.

Question

MHS is selling tickets to its spring musical. On the first day of ticket sales, the school sells 7 adult tickets and 14 student tickets for a total of $252. The school took in $121 on the second day by selling 3 adult tickets and 7 student tickets. Write a system and solve to find the price of an adult ticket and the price of a student ticket.

Answer 1

Let a=price of the adult ticket for each adult
Let s=price of the student ticket for each student

 

Now, write the system of equations:  We have 2 variables and 2 equations.  This is what is needed to solve for the variables.  # of equations must equal # of variables.

 

First day:  7a+14s=252

Second day: 3a+7s=121

 

Solve for a by multiplying the Second day equation above by -2  First, rewrite the equations over.

 

First day:  7a+14s=252

Second day:  -6a-14s=-2*121=-242

 

Now, add the First day and Second day equations to get:

a=10  (the s term drops out because zero times s = zero)

 

Plug a=10 back into either equation and solve for s.

Choose the First day equation:

 

7*10+14s=252

70+14s=252

14s=182

s=13

 

Answers are:

a = $10 = price of adult ticket

s = $13 = price of student ticket