0

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

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!

### 2 Answers by Expert Tutors

Amrutha K. | Patient knowledgeable proven Statistics tutorPatient knowledgeable proven Statistics ...
0
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.

Mark M. | Math Tutor--High School/College levelsMath Tutor--High School/College levels
4.9 4.9 (820 lesson ratings) (820)
0
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??