SOLUTION: Tickets to a local movie were sold at $6 for adults and $4.50 for students. If 63 tickets were sold for a total of $358.50, how many adult tickets were sold?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Tickets to a local movie were sold at $6 for adults and $4.50 for students. If 63 tickets were sold for a total of $358.50, how many adult tickets were sold?      Log On


   

Question 153060: Tickets to a local movie were sold at $6 for adults and $4.50 for students. If 63 tickets were sold for a total of $358.50, how many adult tickets were sold?
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 "63 tickets were sold", this means that the first equation is x%2By=63
Also, because the tickets "were sold at $6 for adults and $4.50 for students" and they collected a "total of $358.50", this means that the second equation is 6x%2B4.5y+=+358.5

60x%2B45y+=+3585 Multiply every term in the second equation by 10 to move the decimal point one spot to the right

So we have the system of equations:


system%28x%2By=63%2C60x%2B45y=3585%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=63 Start with the first equation


y=63-x Subtract x from both sides


y=-x%2B63 Rearrange the equation



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

Since y=-x%2B63, we can now replace each y in the second equation with -x%2B63 to solve for x



60x%2B45highlight%28%28-x%2B63%29%29=3585 Plug in y=-x%2B63 into the first equation. In other words, replace each y with -x%2B63. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



60x%2B%2845%29%28-1%29x%2B%2845%29%2863%29=3585 Distribute 45 to -x%2B63


60x-45x%2B2835=3585 Multiply


15x%2B2835=3585 Combine like terms on the left side


15x=3585-2835Subtract 2835 from both sides


15x=750 Combine like terms on the right side


x=%28750%29%2F%2815%29 Divide both sides by 15 to isolate x



x=50 Divide





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


So the first part of our answer is: x=50









Since we know that x=50 we can plug it into the equation y=-x%2B63 (remember we previously solved for y in the first equation).



y=-x%2B63 Start with the equation where y was previously isolated.


y=-%2850%29%2B63 Plug in x=50


y=-50%2B63 Multiply


y=13 Combine like terms



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


So the second part of our answer is: y=13









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

So our answers are:

x=50 and y=13


So there were 50 adults and 13 students