A professional baseball team sells regular tickets and premium tickets to all of its home games. At a recent game, the average price for a regular ticket was $52.46, and the average price for a premium ticket was $175.85. Which of the following equations shows a relationship where the number of regular tickets, r, and the number of premium tickets, p, that the team sells generates $5,000,000 in ticket sales?Choose 1 answer:(A) 52.46p+175.85r=5,000,000(B) 52.46r+175.85p=5,000,000(C) 52.46p+175.85r=5,000,000(D) 52.46r+175.85p=5,000,000
Q. A professional baseball team sells regular tickets and premium tickets to all of its home games. At a recent game, the average price for a regular ticket was $52.46, and the average price for a premium ticket was $175.85. Which of the following equations shows a relationship where the number of regular tickets, r, and the number of premium tickets, p, that the team sells generates $5,000,000 in ticket sales?Choose 1 answer:(A) 52.46p+175.85r=5,000,000(B) 52.46r+175.85p=5,000,000(C) 52.46p+175.85r=5,000,000(D) 52.46r+175.85p=5,000,000
Set up equation for total revenue: We need to set up an equation that represents the total revenue generated from selling r regular tickets at $52.46 each and p premium tickets at $175.85 each. The total revenue should equal $5,000,000.
Calculate revenue from regular tickets: The revenue from regular tickets can be represented as 52.46×r, or 52.46r. The revenue from premium tickets can be represented as 175.85×p, or 175.85p.
Calculate revenue from premium tickets: Adding these two amounts together gives us the total revenue from ticket sales. So, the equation should be 52.46r+175.85p.
Combine revenue amounts: We set this sum equal to \$\(5\),\(000\),\(000\) to represent the total ticket sales. The equation becomes \(52.46r + 175.85p = 5,000,000\).
Set equation equal to total ticket sales: Now we compare the equation we've derived with the options given in the problem. The correct equation should match the format of the equation we've derived.
Compare equation with options: Option (D) \(52.46r + 175.85p = 5,000,000\) matches the equation we've derived. Therefore, option (D) is the correct answer.
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