Question

tickets at a particular movie theater have different rates for adults and children. On tuesday the theater sold 8 adult tickets and 9 tickets for 174. the next day the theater sold 5 adult tickets and 7 children tickets for 117. What is the price for the adult ticket and the price for the child ticket

Answer 1

Answer:

Adult = $15 pp

Child =  46 pp

Step-by-step explanation:

  Let A and C be the price of Adult and Child's tickets, respectively.

 We can set up equations for each of the two days, Tuesday and Wednesday.  Each equation adds the totals paid for the two ticket levels and set it equal to the total income for that day:

Tues:  8A+9C=174

Wed:   5A+7C=117

We have two equations and two unknowns.  Let's manipulate one of the equations in a way that allows us to eliminate one of the two variables, A or C.  [One can also solve either equation to isolate one of the variables, and then use that in the second equation.]

I chose to multiply the first by 5 and the second by -8, in order to make the coefficients for A the same value in both equations, but opposite in sign:

Tues:   40A+45C   =  870   [Multiply by 5]

Wed:  -40A -56C = -936     [Multiply by -8]

                      -11C = -66      [Add the two equations]

C = 6                                    [Ta Da.  Now use this price for a child's ticket in either of the original equations to find the cost of an adult ticket.]

8A+9C=174

8A+9*(6)=174

8A+54=174

8A   = 120

A  =  15

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Use these two prices in the original equations to see if they indeed add up to the correct totals for each day.

                                                       Total Sales

Price     Tues     Wed          Tues  Wed    

A   15           8          5              120    75

C    6           9            7               54    42

               174        117              174   117 [The prices are correct]

Adult is $15 and child is $6