A 6000 -seat theater has tickets for sale at $$ \$ 26 $$ and $$ \$ 40 $$. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $$ \$ 193,800 $$ ?

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To solve this problem, we need to set up a system of equations based on the given information. Let's denote the number of tickets sold at $26 as $$ x $$ and the number of tickets sold at $40 as $$ y $$.

Given:
1. Total number of tickets sold: $$ x + y = 6000 $$
2. Total revenue: $$ 26x + 40y = 193800 $$

We can solve this system of equations to find the values of $$ x $$ and $$ y $$ that satisfy both conditions.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}x+y=6000\26x+40y=193800\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}x=6000-y\26x+40y=193800\end{array}ight.$$
- step2: Substitute the value of $$x:$$
  $$26\left(6000-yight)+40y=193800$$
- step3: Simplify:
  $$156000+14y=193800$$
- step4: Move the constant to the right side:
  $$14y=193800-156000$$
- step5: Subtract the numbers:
  $$14y=37800$$
- step6: Divide both sides:
  $$\frac{14y}{14}=\frac{37800}{14}$$
- step7: Divide the numbers:
  $$y=2700$$
- step8: Substitute the value of $$y:$$
  $$x=6000-2700$$
- step9: Calculate:
  $$x=3300$$
- step10: Calculate:
  $$\left\{ \begin{array}{l}x=3300\y=2700\end{array}ight.$$
- step11: Check the solution:
  $$\left\{ \begin{array}{l}x=3300\y=2700\end{array}ight.$$
- step12: Rewrite:
  $$\left(x,yight) = \left(3300,2700ight)$$
The solution to the system of equations is $$ x = 3300 $$ and $$ y = 2700 $$.

Therefore, to generate a total revenue of $193,800, the theater should sell 3300 tickets at $26 and 2700 tickets at $40 for a sellout performance.
The theater should sell 3300 tickets at $26 and 2700 tickets at $40 to reach a total revenue of $193,800.

A 6000 -seat theater has tickets for sale at and . How many tickets should be sold at each price for a sellout performance to generate a total revenue of ?

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