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?

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) (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
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

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:

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

Start with the first equation

Subtract from both sides

Rearrange the equation

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

Since , we can now replace each in the second equation with to solve for

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Combine like terms on the left side

Subtract 2835 from both sides

Combine like terms on the right side

Divide both sides by 15 to isolate x

Divide

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

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms

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

So the second part of our answer is:

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

So our answers are:

and

So there were 50 adults and 13 students

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