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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.

RainbowPanda  Aug 29, 2018
 #1
avatar+91381 
+1

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

 

cool cool cool

CPhill  Aug 29, 2018
edited by CPhill  Aug 29, 2018
 #2
avatar+2072 
+2

Oh oops forgot to put those in, my bad >.<

6A+B=23

12A+14B=106

RainbowPanda  Aug 29, 2018
 #3
avatar+91381 
+2

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"   ????

 

 

cool cool cool

CPhill  Aug 29, 2018
 #4
avatar+2072 
+1

Not sure what to do after that. 12A+14(23-6A)=106

RainbowPanda  Aug 29, 2018
 #5
avatar+91381 
+2

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  ???

 

 

cool cool cool

CPhill  Aug 29, 2018
 #6
avatar+2072 
0

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
avatar+2072 
+1

Hold on b can't be -1 can it...?

RainbowPanda  Aug 29, 2018
 #9
avatar+91381 
+2

Whoops...now I made an error...!!!!

 

[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...!!!

 

 

cool cool cool

CPhill  Aug 29, 2018
 #12
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+2

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

Guest Aug 29, 2018
 #8
avatar+2072 
+1

Oh hold on would A=3 and B=5

RainbowPanda  Aug 29, 2018
 #10
avatar+91381 
+1

You are correct....!!!....good job  !!!

 

 

cool cool cool

CPhill  Aug 29, 2018
 #11
avatar+2072 
+1

Thank you for your help once again!

RainbowPanda  Aug 29, 2018

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