Word problem

Question

THE theater sells 3 types of tickets: general admission, senior citizen and child. Mark bought 9 general admission, 2 senior citizen and 3 child tickets for 170$. Sarah bought 5 general admission, 4 senior citizen and 7 child tickets and paid $173. Kyle bought 4 general admission, 1 senior citizen and 6 child tickets and paid 116.50. Find the cost of each type of ticket. 

Answer 1

g = cost of general admission

s = cost of senior admission

c = cost of child admission

 

9g + 2s + 3c = 170      {equation 1 - Mark}

5g + 4s + 7c = 173      {equation 2 - Sarah}

4g + s + 6c = 116.5     {equation 3 - Kyle}

 

Let's eliminate a variable and create 2 equations with 2 unknowns.

Easiest to eliminate appears to be the s variable.

Using equation 1 and equation 2 multiply equation 1 through by -2 and

add the two equations.

 

-18g - 4s - 6c = -340

   5g + 4s + 7c = 173      

--------------------------

-13g + c = = -167

 

Multiply equation 3 by -2 and add to equation 1:

 9g + 2s + 3c = 170      

-8g - 2s - 12c = -233

---------------------------

g - 9c = -63

 

We now have 2 equations with 2 unknowns we can use to find the

value of g and c

 

-13g + c = -167

     g - 9c = -63

 

multiply first equation by 9 and add equations

 

-117g + 9c = -1503

      g - 9c = -63

-------------------------

-116g = -1566

g = -1566/(-116)

g = 13.5

 

g - 9c = -63

13.5 - 9c = -63

-9c = -76.5

c = -76.5/(-9)

c = 8.5
 

We now have the price of a general admission ticket ($13.50)

and the price of a child's ticket ($8.50).  Plug those two values

into one of the original 3 equations and solve for s to fine the

cost of a senior admission ticket.