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**+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

CPhill
Aug 29, 2018

#3**+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" ????

CPhill
Aug 29, 2018

#5**+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 ???

CPhill
Aug 29, 2018

#6**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

#9**+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...!!!

CPhill
Aug 29, 2018