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

Algebra ->  Systems-of-equations -> 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       Log On


   

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) About Me  (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 x%2By=650. 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 7.5x%2B3.5y=4375. This is our second equation.


10%287.5x%2B3.5y%29=10%284375%29 Multiply both sides of the second equation by 10. This will make every number a whole number.


75x%2B35y=43750 Distribute and multiply.






So we now have this system of equations:

system%28x%2By=650%2C75x%2B35y=43750%29


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

x%2By=650 Start with the first equation


y=650-x Subtract x from both sides


y=-x%2B650 Rearrange the equation


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

Since y=-x%2B650, we can now replace each y in the second equation with -x%2B650 to solve for x



75x%2B35highlight%28%28-x%2B650%29%29=43750 Plug in y=-x%2B650 into the first equation. In other words, replace each y with -x%2B650. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



75x%2B%2835%29%28-1%29x%2B%2835%29%28650%29=43750 Distribute 35 to -x%2B650


75x-35x%2B22750=43750 Multiply


40x%2B22750=43750 Combine like terms on the left side


40x=43750-22750Subtract 22750 from both sides


40x=21000 Combine like terms on the right side


x=%2821000%29%2F%2840%29 Divide both sides by 40 to isolate x



x=525 Divide





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


So the first part of our answer is: x=525









Since we know that x=525 we can plug it into the equation y=-x%2B650 (remember we previously solved for y in the first equation).



y=-x%2B650 Start with the equation where y was previously isolated.


y=-%28525%29%2B650 Plug in x=525


y=-525%2B650 Multiply


y=125 Combine like terms



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


So the second part of our answer is: y=125









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

So our answers are:

x=525 and y=125



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