Ticket Prices Two hundred tickets were sold for a

baseball game, which amounted to $840. Student
tickets cost $3, and adult tickets cost $5.
(a) Let x be the number of student tickets sold and y
be the number of adult tickets sold. Write a system
of linear equations whose solution gives the
number of each type of ticket sold.
(b) Use the method of substitution to solve the system.

x + y = 200

3 x + 5 y = 840
so
y = (200-x)
substitute (200-x) for y
3 x + 5 (200-x) = 840

3 x + 1000 - 5 x = 840

2 x = 160
x = 80
y = 120

Can you explain how to factor the following trinomials forms: x2 + bx + c and ax2 + bx + c. Can there be more than one way to factor a problem like this? can you please show it in written word and step by step?

To solve this problem, we need to set up a system of linear equations based on the given information.

Let x be the number of student tickets sold and y be the number of adult tickets sold.

(a) Writing a system of linear equations:
We know that 200 tickets were sold in total, so we can set up the first equation based on this information:
x + y = 200 -- Equation 1

We also know that the total amount generated from ticket sales was $840. The revenue from student tickets at $3 per ticket is 3x, and the revenue from adult tickets at $5 per ticket is 5y. So, we can set up the second equation based on this information:
3x + 5y = 840 -- Equation 2

(b) Using the method of substitution to solve the system:
From Equation 1, we can rewrite it as:
x = 200 - y

Now, substitute this value of x in Equation 2:
3(200 - y) + 5y = 840

Simplify this equation:
600 - 3y + 5y = 840
2y = 840 - 600
2y = 240
y = 240/2
y = 120

Substitute this value of y back into Equation 1:
x + 120 = 200
x = 200 - 120
x = 80

Therefore, the solution to the system of linear equations is x = 80 and y = 120. This means that 80 student tickets and 120 adult tickets were sold.