Answer:
3600 $10 tickets
4900 $20 tickets
Step-by-step explanation:
We can use variables to represent the different types of tickets. Let "x" represent the amount of $10 tickets and "y" represent the amount of $20 tickets. Now we can set up a system of equations.
<h3>Setting up a System of Equations</h3>
We know that in total, 8500 tickets were sold. Therefore...
![x+y=8500](https://tex.z-dn.net/?f=x%2By%3D8500)
Or in other words, "the amount of $10 tickets plus the amount of $20 tickets is equivalent to 8500 tickets in total".
We also know that $134,000 was made. Therefore...
![10x+20y=134000](https://tex.z-dn.net/?f=10x%2B20y%3D134000)
Or in other words, "10 times the amount of $10 tickets plus the 20 times the amount of $20 tickets is equivalent to 134000". Notice that since each ticket costs $10/$20, we have to multiply each variable by that value. We can now solve this system of equations.
<h3>Solving the System of Equations</h3>
![x+y=8500\\10x+20x=134000](https://tex.z-dn.net/?f=x%2By%3D8500%5C%5C10x%2B20x%3D134000)
We can solve this system of equations using the elimination method. First, make either the x or y value equivalent in both equations. To do this, we can multiply a whole equation by a certain value.
Multiply the first equation by 10:
![10x+10y=85000\\10x+20y=134000](https://tex.z-dn.net/?f=10x%2B10y%3D85000%5C%5C10x%2B20y%3D134000)
Now, subtract the first equation from the second equation.
![10y=49000](https://tex.z-dn.net/?f=10y%3D49000)
Divide both sides of the equation by 10
![y=4900](https://tex.z-dn.net/?f=y%3D4900)
Now, subtract this number from 8500 to find the amount of $10 tickets.
![8500-4900=3600](https://tex.z-dn.net/?f=8500-4900%3D3600)
The jazz concert sold 3600 $10 tickets and 4900 $20 tickets.