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?

Algebra ->  Coordinate Systems and Linear Equations -> 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?      Log On


   

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) About Me  (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:

system%28x%2By=340%2C2x%2B3y=810%29


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

x%2By=340 Start with the first equation


y=340-x Subtract x from both sides


y=-x%2B340 Rearrange the equation


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

Since y=-x%2B340, we can now replace each y in the second equation with -x%2B340 to solve for x



2x%2B3highlight%28%28-x%2B340%29%29=810 Plug in y=-x%2B340 into the first equation. In other words, replace each y with -x%2B340. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



2x%2B%283%29%28-1%29x%2B%283%29%28340%29=810 Distribute 3 to -x%2B340


2x-3x%2B1020=810 Multiply


-x%2B1020=810 Combine like terms on the left side


-x=810-1020Subtract 1020 from both sides


-x=-210 Combine like terms on the right side


x=%28-210%29%2F%28-1%29 Divide both sides by -1 to isolate x



x=210 Divide





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


So the first part of our answer is: x=210









Since we know that x=210 we can plug it into the equation y=-x%2B340 (remember we previously solved for y in the first equation).



y=-x%2B340 Start with the equation where y was previously isolated.


y=-%28210%29%2B340 Plug in x=210


y=-210%2B340 Multiply


y=130 Combine like terms



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


So the second part of our answer is: y=130









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

So our answers are:

x=210 and y=130 which means that 210 $2 tickets and 130 $3 tickets were sold