SOLUTION: For a school play, 340 tickets with a total value of $810 were sold. Some tickets cost $2 and some cost $3. How many of each type were sold?

Question 153084: For a school play, 340 tickets with a total value of $810 were sold. Some tickets cost $2 and some cost $3. How many of each type were sold?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=# of $2 tickets and y=# of $3 tickets

First translate the word problem into the system of equations:

Let's use substitution to solve the system

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 1020 from both sides

Combine like terms on the right side

Divide both sides by -1 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 which means that 210 $2 tickets and 130 $3 tickets were sold

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