Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. The box office at a theater is selling tickets for a series of rock concerts. So far, they have sold 94 balcony tickets and 99 general admission floor tickets for Friday's show, for a total of $7,660 in receipts. For Saturday's show, 61 balcony tickets and 59 general admission floor tickets have been sold, equaling $4,824 in receipts. How much does each ticket cost? A balcony seat ticket costs $_____, and a general admission floor ticket costs $_____.

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.  The box office at a theater is selling tickets for a series of rock concerts. So far, they have sold 94 balcony tickets and  99 general admission floor tickets for Friday's show, for a total of $7,660 in receipts. For Saturday's show, 61 balcony tickets and  59 general admission floor tickets have been sold, equaling $4,824 in receipts. How much does each ticket cost?  A balcony seat ticket costs $_____, and a general admission floor ticket costs $_____.

Bytelearn · Accepted Answer

Define Variables: Let's denote the price of a balcony seat ticket as b and the price of a general admission floor ticket as f. We are given that 94 balcony tickets and 99 general admission floor tickets for Friday's show have been sold for a total of $7,660. This gives us the equation 94b + 99f = 7660.Equations for Friday's Show: For Saturday's show, 61 balcony tickets and 59 general admission floor tickets have been sold for a total of $4,824. This gives us the equation 61b + 59f = 4824.Eliminate Variable f: We now have a system of two equations. We need to eliminate one of the variables, b or f. We choose to eliminate f because its coefficients are close in value, which might make the calculations simpler.New Equations: To eliminate f, we can multiply the second equation by 99 and the first equation by 59, the coefficients of f in the opposite equations. This gives us the new equations 6039b + 5841f = 476376 and 5546b + 5831f = 451940.Solve for b: We now subtract the second new equation from the first new equation to eliminate f. This gives us 493b = 24436. Substitute b into Equation: We divide both sides of the equation by 493 to solve for b. This gives us b = 24436 / 493, which simplifies to b = 49.57. Since ticket prices are typically whole numbers, we can round this to b = 50.Solve for f: We substitute b = 50 into the first original equation and solve for f. This gives us 94*50 + 99f = 7660, which simplifies to 4700 + 99f = 7660.We subtract 4700 from both sides of the equation to solve for f. This gives us 99f = 2960, and dividing both sides by 99 gives us f = 2960 / 99, which simplifies to f = 29.90. Rounding to the nearest whole number, we get f = 30.

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