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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineThe box office at a theater is selling tickets for a series of rock concerts. So far, they have sold 4848 balcony tickets and 9090 general admission floor tickets for Friday's show, for a total of $3,798\$3,798 in receipts. For Saturday's show, 3535 balcony tickets and 8181 general admission floor tickets have been sold, equaling $3,123\$3,123 in receipts. How much does each ticket cost?\newlineA balcony seat ticket costs $_\$\_, and a general admission floor ticket costs $_\$\_.

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineThe box office at a theater is selling tickets for a series of rock concerts. So far, they have sold 4848 balcony tickets and 9090 general admission floor tickets for Friday's show, for a total of $3,798\$3,798 in receipts. For Saturday's show, 3535 balcony tickets and 8181 general admission floor tickets have been sold, equaling $3,123\$3,123 in receipts. How much does each ticket cost?\newlineA balcony seat ticket costs $_\$\_, and a general admission floor ticket costs $_\$\_.
  1. Define Variables: Let xx represent the cost of a balcony seat ticket and yy represent the cost of a general admission floor ticket.\newlineFirst equation based on Friday's show: 48x+90y=379848x + 90y = 3798
  2. First Equation: Second equation based on Saturday's show: 35x+81y=312335x + 81y = 3123
  3. Second Equation: System of equations:\newline48x+90y=379848x + 90y = 3798\newline35x+81y=312335x + 81y = 3123\newlineWe need to solve this system for xx and yy.
  4. Solve System: Multiply the second equation by 4848 and the first equation by 3535 to align the coefficients of xx for elimination:\newline(35x+81y)×48=3123×48(35x + 81y) \times 48 = 3123 \times 48\newline(48x+90y)×35=3798×35(48x + 90y) \times 35 = 3798 \times 35
  5. Multiply Equations: After multiplication, the system of equations becomes:\newline1680x+3888y=1499041680x + 3888y = 149904\newline1680x+3150y=1329301680x + 3150y = 132930
  6. Subtract Equations: Subtract the second equation from the first to eliminate xx:
    (1680x+3888y)−(1680x+3150y)=149904−132930(1680x + 3888y) - (1680x + 3150y) = 149904 - 132930
    1680x+3888y−1680x−3150y=169741680x + 3888y - 1680x - 3150y = 16974
    738y=16974738y = 16974
  7. Solve for y: Solve for y:\newline738y=16974738y = 16974\newliney=16974738y = \frac{16974}{738}\newliney=23y = 23
  8. Substitute and Solve: Substitute y=23y = 23 into one of the original equations to solve for xx. We'll use the first equation:\newline48x+90(23)=379848x + 90(23) = 3798
  9. Calculate x: Calculate the value of x:\newline48x+2070=379848x + 2070 = 3798\newline48x=3798−207048x = 3798 - 2070\newline48x=172848x = 1728\newlinex=172848x = \frac{1728}{48}\newlinex=36x = 36

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