SOLUTION: Hi, I have the answers to the problems but I don't know the steps to get the answer here are a few of my word problems and answers. If someone could help me out with the formula t

Question 143643: Hi, I have the answers to the problems but I don't know the steps to get the answer here are a few of my word problems and answers. If someone could help me out with the formula to answer the problem it would be greatly appreciated.
Six hundred people attened the premiere of a motion picture. Adult tickets cost $9, and chilren were admitted for $6. If box office reciepts totaled $4800, how many chilren attended the premiere?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=# of children, y=# of adults

Since "Six hundred people attened the premiere", this means that the total of children and adults is 600. So the first equation is:

Also, since "Adult tickets cost $9, and chilren were admitted for $6" and the theater pulled in $4,800, this tells us that the second equation is:

So this gives us this system of equations:

Let's use substitution to solve this 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

Divide both sides by

Break up the fraction

Reduce

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

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 5400 from both sides

Combine like terms on the right side

Divide both sides by -3 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 200 children and 400 adults attended

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