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Answer:
x = 2y
64x + 132y = 1040
Cost of each adult ticket = $4
Cost of each student ticket = $8
Step-by-step explanation:
Given the $1,040 total earnings of a drama club, in which they sold 64 adult tickets and 132 student tickets.
Let x = student tickets
y = adult tickets
We can algebraically represent the first part of the given problem as:
64x + 132y = 1040
We're also given the information that the each adult ticket costs twice as much as the students' price for each ticket. An algebraic representation of this statement is: x = 2y.
In order to determine the cost of each adult and student tickets, we can use the substitution method by substituting the value of x = 2y into the first equation:
x = 2y
64x + 132y = 1040
64(2y) + 132y = 1040
Distribute 64 into the parenthesis:
128y + 132y = 1040
260y = 1040
Divide both sides by 260 to solve for y:
[tex]\frac{260y}{260} = \frac{1040}{260}[/tex]
y = 4 ⇒ This is the cost of each adult ticket.
Next, substitute the value of y into the second equation, x = 2y, to solve for the cost of each student ticket.
x = 2y
x = 2(4)
x = 8 ⇒ This is the cost of each student ticket.
Therefore, the cost each adult ticket is $4, while the cost of each student ticket is $8.