SOLUTION: The drama club sold 1,500 tickets for the end-of-year-performance. Admission prices were $12 for adults and $6 for students. The total amount collected at the box office was $16,20

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The drama club sold 1,500 tickets for the end-of-year-performance. Admission prices were $12 for adults and $6 for students. The total amount collected at the box office was $16,20      Log On


   

Question 153059: The drama club sold 1,500 tickets for the end-of-year-performance. Admission prices were $12 for adults and $6 for students. The total amount collected at the box office was $16,200. How many students attended the play?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=# of adults and y=# of students

Since the "drama club sold 1,500 tickets", this means that the first equation is x%2By=1500

Since the "Admission prices were $12 for adults and $6 for students" and because they collected $16,200, this means that the second equation is 12x%2B6y=16200

So we have the system of equations:

system%28x%2By=1500%2C12x%2B6y=16200%29



Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

x%2By=1500 Start with the first equation


y=1500-x Subtract x from both sides


y=-x%2B1500 Rearrange the terms



---------------------

Since y=-x%2B1500, we can now replace each y in the second equation with -x%2B1500 to solve for x



12x%2B6highlight%28%28-x%2B1500%29%29=16200 Plug in y=-x%2B1500 into the first equation. In other words, replace each y with -x%2B1500. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



12x%2B%286%29%28-1%29x%2B%286%29%281500%29=16200 Distribute 6 to -x%2B1500


12x-6x%2B9000=16200 Multiply


6x%2B9000=16200 Combine like terms on the left side


6x=16200-9000Subtract 9000 from both sides


6x=7200 Combine like terms on the right side


x=%287200%29%2F%286%29 Divide both sides by 6 to isolate x



x=1200 Divide





-----------------First Answer------------------------------


So the first part of our answer is: x=1200









Since we know that x=1200 we can plug it into the equation y=-x%2B1500 (remember we previously solved for y in the first equation).



y=-x%2B1500 Start with the equation where y was previously isolated.


y=-%281200%29%2B1500 Plug in x=1200


y=-1200%2B1500 Multiply


y=300 Combine like terms



-----------------Second Answer------------------------------


So the second part of our answer is: y=300









-----------------Summary------------------------------

So our answers are:

x=1200 and y=300


So 1,200 adults and 300 students attended