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# Another word problem

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Sumalee's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 6 adult tickets and 1 student ticket for a total of \$23. The school took in \$106 on the second day by selling 12 adult tickets and 14 student tickets. Find the price of an adult ticket and the price of a student ticket.

Aug 29, 2018

#1
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Can you set up the equations, RP???

[ Hint ...let the number of adult tickets be "A"  and the number of student tickets  be  "B" ]

EDIT...sorry  A should be the cost of an adult ticket and  B the cost of a student ticket

Aug 29, 2018
edited by CPhill  Aug 29, 2018
#2
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Oh oops forgot to put those in, my bad >.<

6A+B=23

12A+14B=106

RainbowPanda  Aug 29, 2018
#3
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OK...good job...look at your first equation...can't we rearrange it so that we have

B  = 23  - 6A       ???

Knowing this...can you sub it into the second for  "B"   ????

CPhill  Aug 29, 2018
#4
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Not sure what to do after that. 12A+14(23-6A)=106

RainbowPanda  Aug 29, 2018
#5
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OK...just simplify this

12A+14(23-6A)=106

12A  + 14*23  - 14*6A  = 106

12A  + 322 - 84A   = 106

-72A + 322  = 106   subtract 322 from each side

-72A  = - 216   divide both sides by -72

A  = 4    =   [4\$ for an adult ticket ]

Now...put  4  bacK into   23  - 6A  to find the cost of a child's ticket  since  B = 23 - 6A

Does that make sense  ???

CPhill  Aug 29, 2018
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Is it bad that I actually knew that but didn't fully process it in my head til I saw it typed out. Like it totally makes sense and I felt like I already had the answers.. lol

So B= -1

RainbowPanda  Aug 29, 2018
#7
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Hold on b can't be -1 can it...?

RainbowPanda  Aug 29, 2018
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[Trying to do math in my head....never a good idea  !!! ]

-72A  = - 216   divide both sides by -72

A  = 3    =   [\$3  for adult tickets]

Putting this back into  23 - 6A    =  23 - 6(3) = 23  - 18  =  \$5  for child's ticket

But...you had the right idea...that was my stupid error...!!!

CPhill  Aug 29, 2018
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Negative price tickets will happen for musicals when the singing is really, really bad. Free ear plugs are included.

Guest Aug 29, 2018
#8
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Oh hold on would A=3 and B=5

Aug 29, 2018
#10
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You are correct....!!!....good job  !!!

CPhill  Aug 29, 2018
#11
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Thank you for your help once again!

RainbowPanda  Aug 29, 2018