AUse the information from the exercise to create two equations and then combine them into a system.
BUse the Substitution Method to solve the system of equations created in Part A.
Ax=2y & (I) 64x+132y=1040 & (II)
B$ 8 for an adult ticket, $ 4 for a student ticket
Practice makes perfect
We want to create a system of linear equations to represent the earnings of a drama club from a production. Let's use x to represent the price of an adult ticket and y to represent the price of a student ticket. From the exercise we know that an adult ticket costs twice as much as a student ticket.
x=2 y
We also know that the club earned a total of $ 1040 by selling 64 adult tickets at price x and 132 student tickets at price y.
64* x+ 132 * y= 1040
Now we can create a system of equations by combining the two equations we created.
x=2y & (I) 64x+132y=1040 & (II)
We want to know how much each ticket costs. We can find this out if we solve the system of equations we created in Part A.
x=2y & (I) 64x+132y=1040 & (II)
We will use the Substitution Method to solve the system. Notice that Equation (I) is already solved for x. Because of this, we will substitute 2y for x in Equation (II) and solve it for y. Let's do it!
Now that we have a value for y, we can substitute its value for y in either equation and solve for x. Let's substitute 4 for y in Equation (I) for simplicity.
