Question

suppose that there are two types of tickets to a show: advance and same - day. the combined cost of one advance ticket and one same - day ticket is $55. for one performance, 40 advance tickets and 35 same - day tickets were sold. the total amount paid for the tickets was $2125. what was the price of each kind of ticket? advance ticket: $ same - day ticket: $

Explanation:

Step1: Define Variables

Let \( x \) be the price of an advance ticket (in dollars) and \( y \) be the price of a same - day ticket (in dollars).
We know two things:

1. The combined cost of one advance ticket and one same - day ticket is $55, so we have the equation \( x + y=55 \).
2. 40 advance tickets and 35 same - day tickets were sold for a total of $2125, so we have the equation \( 40x + 35y=2125 \).

Step2: Solve the System of Equations

From the first equation \( x + y=55 \), we can express \( y \) in terms of \( x \) as \( y = 55 - x \).
Substitute \( y = 55 - x \) into the second equation \( 40x+35y = 2125 \):

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Step3: Find the Value of \( y \)

Substitute \( x = 40 \) into \( y=55 - x \):
\( y=55 - 40=15 \)

Answer:

Advance ticket: $\boldsymbol{40}$
Same - day ticket: $\boldsymbol{15}$