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.
Setting up a System of Equations
We know that in total, 8500 tickets were sold. Therefore...
[tex]x+y=8500[/tex]
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...
[tex]10x+20y=134000[/tex]
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.
Solving the System of Equations
[tex]x+y=8500\\10x+20x=134000[/tex]
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:
[tex]10x+10y=85000\\10x+20y=134000[/tex]
Now, subtract the first equation from the second equation.
[tex]10y=49000[/tex]
Divide both sides of the equation by 10
[tex]y=4900[/tex]
Now, subtract this number from 8500 to find the amount of $10 tickets.
[tex]8500-4900=3600[/tex]
The jazz concert sold 3600 $10 tickets and 4900 $20 tickets.
