Write a System of Equations to solve the following problem:

The school that Maria goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 1 senior citizen ticket and 12 student tickets for a total of $51. The school took in $93 on the second day by selling 5 senior citizen tickets and 6 student tickets. What is the price each of one senior citizen ticket and one student ticket?

Cost of Senior Citizen Ticket: $

Cost of Student Ticket: $

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mathstudent55 mathstudent55 · Answer 1 · 2021-03-01T22:52:44+01:00

Answer:

Cost of Senior Citizen Ticket: $15

Cost of Student Ticket: $3

Step-by-step explanation:

Let the price of a senior citizen ticket be s.

Let the price of a student ticket be t.

Day 1:

s + 12t = 51

Day 2:

5s + 6t = 93

The system of equations is:

s + 12t = 51

5s + 6t = 93

Let's use the substitution method to solve it. Solve the first equation for s.

s = 51 - 12t

Now substitute s in the second equation with 51 - 12t.

5s + 6t = 93

5(51 - 12t) + 6t = 93

255 - 60t + 6t = 93

Subtract 255 from both sides. Combine -60t and 6t.

-54t = -162

Divide both sides by -54.

t = 3

Now substitute 3 for t in the equation

s = 51 - 12t

s = 51 - 12(3)

s = 51 - 36

s = 15

Answer:

Cost of Senior Citizen Ticket: $15

Cost of Student Ticket: $3