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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!
Jul 27 | Connor from Overland Park, KS

2 Answers by Expert Tutors

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Amrutha K. | Patient knowledgeable proven Statistics tutorPatient knowledgeable proven Statistics ...
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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.
 
 
 
Jul 27 | Amrutha K.
Mark M. | Math Tutor--High School/College levelsMath Tutor--High School/College levels
4.9 4.9 (820 lesson ratings) (820)
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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??
 
          
Jul 27 | Mark M.

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