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Arjun's school is selling tickets to a fall musical. On the first day of ticket sales the school sold 8 senior citizen tickets and 9 student tickets for a total of $169. The school took in $149 on the second day by selling 7 senior citizen tickets and 8 student tickets. What is the price each of one senior citizen ticket and one student ticket? Explain?

 Feb 27, 2020
 #1
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Let the price of a senior citizen's ticket = N

Let the price of a student's ticket           = S

 

8N  +  9S =169.......................(1)

7N  +  8S =149.......................(2), solve for N, S

 

N = $11.00 price of senior citizen's ticket

S =$9.00 price of a student's ticket.

 Feb 27, 2020
 #2
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Let  x  =  price of one senior citizen ticket.

Let  y =   price of one student ticket.

 

8x + 9y  =  169     --->   (multiply by 8)    --->    64x + 72y  =  1352

7x + 8y  =  149     --->   (multiply by -9)   --->   -63x - 72y  =  -1341

(adding down the columns)                     --->        x            =      11    <---   cost of one senior citizen ticket.

 

Since  x = 11    --->     8x + 9y  =  169     --->     8(11) + 9y  =  169     --->     88 + 9y  =  169

(subtracting 88 from both sides)                                                                             9y  =  81

                                                                               cost of one student ticket   --->   y  =  9

 Feb 27, 2020

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