(2) A local theater sells both regular priced admission tickets for their evening movies and reduced priced admission ticiets for thelr earrier matinee shows. Over the course of one business day, the theater earned $6,721 in revenue and sold 558 total tickets. Find how many of each type of ticket, was sold if regular price admission is $13.50 and tickets for matinee times are $6.50.

Question

(2) A local theater sells both regular priced admission tickets for their evening movies and reduced priced admission ticiets for thelr earrier matinee shows. Over the course of one business day, the theater earned  $6,721 in revenue and sold 558 total tickets. Find how many of each type of ticket, was sold if regular price admission is  $13.50 and tickets for matinee times are  $6.50.

Bytelearn · Accepted Answer

Define variables:  Let r be the number of regular tickets and m be the number of matinee tickets sold. Write total tickets equation:  We know the total number of tickets sold is 558, so we write the equation: r + m = 558. Write revenue equation:  The total revenue from the tickets is $6,721. Using the prices, the revenue equation is 13.50r + 6.50m = 6721. Solve for r:  Solve the system of equations. Start by solving the first equation for r: r = 558 - m. Substitute r in revenue equation:  Substitute r in the revenue equation: 13.50(558 - m) + 6.50m = 6721. Simplify and solve for m:  Simplify and solve for m: 7533 - 13.50m + 6.50m = 6721, which simplifies to -7m = -812. Find value of m:  Solve for m: m = 116. Find value of r:  Substitute m back into the equation for r: r = 558 - 116 = 442.

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