The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales, the school sold 7 senior citizen tickets and 5 child tickets for a total of \( \$ \) 163. The school took in \( \$ 68 \) on the second day by selling 3 senior citizen tickets and 2 child tickets. We are interested in finding the price of a senior ticket and a child ticket using a system of equations. Use the information provided to answer the following questions: (a) Identify what \( x \) and \( y \) should represent in this situation. A \[ \boldsymbol{x}=\text { total number of attendees. } \] \[ y=\text { total revenue. } \] B \( \boldsymbol{x}= \) price of a senior citizen ticket. \( \boldsymbol{y}= \) price of a child ticket. c \( x= \) senior citizen. \( y= \) child. D \( x= \) number of senior citizen tickets sold. \( y= \) number of child tickets sold. (b) Translate the first sentence: "On the first day, the school sold 7 senior citizen tickets and 5 child tickets for a total of \( \$ 163 \) ", into a math equation.
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First, let's clarify what the variables represent. In this case, the best choice is option **B**: \( \boldsymbol{x} \) represents the price of a senior citizen ticket, and \( \boldsymbol{y} \) represents the price of a child ticket. This helps lay the groundwork for our equations as we analyze the ticket sales. Now, to translate the first sentence into a math equation, we can express it as follows: \[ 7x + 5y = 163 \] Here, 7 represents the number of senior citizen tickets sold, \( x \) is the price of each senior citizen ticket, 5 is the number of child tickets sold, and \( y \) is the price of each child ticket, totaling \( \$ 163 \). It's like cracking a code to find the prices hidden beneath the ticket sales!
