The school that Dan goes to is selling tickets to a play

Question

The school that Dan goes to is selling tickets to a play. On the first day of ticket sales the school sold 6
adult tickets and 16 student tickets for a total of $312. The school took in $189 on the second day by
selling 7 adult tickets and 7 student tickets. Find the price of an adult ticket and the price of a student
ticket. 

I don't know how to solve this using elimination, which I have to do.

Thanks!

Answer 1

Let ‘x’ be the price of adult ticket.

Let ‘y’ be the price of student ticket.

 

On the first day, 6 adult tickets and 16 student tickets were sold and the total ticket sales was $312.

that is: 6x+16y=312    ————equation 1

 

On the Second day, 7 adult tickets and 7 student tickets were sold and the total ticket sales was $189.
that is: 7x+7y=189       ————equation 2

 

Solving equations 1 and 2,

 

Multiplying 1st equation with 7 on both sides: 

7(6x+16y=312)

42x+112y=2184  ———equation 3

 

Multiplying 2nd equat with 6 on both sides:

6(7x+7y=189)

42x+42y=1134. ———-equation 4

Multiplying equation 4 with ‘-‘ (minus) on both sides:

-42x-42y=-1134

solving equation 3 and 4:

42x+112y=2184

-42x-42y=-1134

—————————-

70y=1050

 

y=1050/70

y=15

 

therefore, price of student ticket ‘y’ is $15.

 

now substitute this y value in any of the equations above to get x value.

lets take equation 2:

7x+7y=189

 

7x+7*15=189

7x+105=189

7x=189-105

7x=84

x=84/7=12

 

therefore, price of adult ticket ‘x’ is 12.

 

 

 

Answer 2

Let x = price of a student ticket and y = price of adult ticket

 

Then  16x + 6y = 312

           7x + 7y = 189

 

To eliminate y, multiply the first equation by -7 and he second equation by 6 to get:

 

         -112x -42y = -2184

            42x+42y =  1134

 

Add the equations:  -70x = -1050

 

                                  x = $15.00

 

Substitute back into one of the original equations:  7(15.00) + 7y = 189

 

                                                                                          7y = 84

 

                                                                                            y = $12

 

Each student ticket costs $15 and each adult ticket costs $12.Usually, student tickets are cheaper than adult tickets??