SOLUTION: I need help...Please:) Page 504 Number 4 I have to solve using two equations with two variables. High School Musical El/ segundo High School put on their annual musical. The

Question 145298This question is from textbook Beginning Algebra
: I need help...Please:)
Page 504
Number 4
I have to solve using two equations with two variables.
High School Musical El/ segundo High School put on their annual musical. The students sold 650 tickets for a value of $4375.000. If orchestra seats cost $7.50 and balcony seats cost $3.50, how many of each kind of seat were sold? This question is from textbook Beginning Algebra

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=# of orchestra seats and y=# of balcony seats

Since the "students sold 650 tickets", this means that . This is our first equation.

Also, since the total cost of x orchestra seats (at $7.50) and y balcony seats (at $3.50) is $4,375.00, this means that . This is our second equation.

Multiply both sides of the second equation by 10. This will make every number a whole number.

Distribute and multiply.

So we now have 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

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

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 22750 from both sides

Combine like terms on the right side

Divide both sides by 40 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

This means that the students sold 525 orchestra seats and 125 balcony seats
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