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A minor league hockey team has been collecting ticket sales data over the past year. At a current price of $25 per ticket, an average of 4000 seats are purchased. The team predicts that for each $1 increase in ticket price, 100 fewer tickets will be sold. Which of the following functions best models the amount of money that the hockey team expects to collect from ticket sales, y, based on an $x increase in ticket price? Choose 1 answer: (A) y=(25+x)(4000-100 x) (B) y=(25-x)(4000+100 x) (C) y=x(4000-100 x) (D) y=4000(25+x)

A minor league hockey team has been collecting ticket sales data over the past year. At a current price of $25 \$ 25 per ticket, an average of 40004000 seats are purchased. The team predicts that for each $1 \$ 1 increase in ticket price, 100100 fewer tickets will be sold. Which of the following functions best models the amount of money that the hockey team expects to collect from ticket sales, y y , based on an $x \$ x increase in ticket price?\newlineChoose 11 answer:\newline(A) y=(25+x)(4000−100x) y=(25+x)(4000-100 x) \newline(B) y=(25−x)(4000+100x) y=(25-x)(4000+100 x) \newline(C) y=x(4000−100x) y=x(4000-100 x) \newline(D) y=4000(25+x) y=4000(25+x)

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Q. A minor league hockey team has been collecting ticket sales data over the past year. At a current price of $25 \$ 25 per ticket, an average of 40004000 seats are purchased. The team predicts that for each $1 \$ 1 increase in ticket price, 100100 fewer tickets will be sold. Which of the following functions best models the amount of money that the hockey team expects to collect from ticket sales, y y , based on an $x \$ x increase in ticket price?\newlineChoose 11 answer:\newline(A) y=(25+x)(4000−100x) y=(25+x)(4000-100 x) \newline(B) y=(25−x)(4000+100x) y=(25-x)(4000+100 x) \newline(C) y=x(4000−100x) y=x(4000-100 x) \newline(D) y=4000(25+x) y=4000(25+x)
  1. Ticket Price Relationship: For every $1\$1 increase in ticket price, the number of tickets sold decreases by 100100. So if the ticket price increases by xx dollars, the new ticket price is $25+x\$25 + x.
  2. New Tickets Sold Calculation: The new number of tickets sold would be 4000−100x4000 - 100x because for each dollar increase, 100100 fewer tickets are sold.
  3. Total Revenue Calculation: To find the total revenue, yy, we multiply the new ticket price by the new number of tickets sold: y=(25+x)(4000−100x)y = (25 + x)(4000 - 100x).
  4. Correct Function Identification: Check the answer choices to see which one matches our equation. The correct function is y=(25+x)(4000−100x)y = (25 + x)(4000 - 100x), which is option (A).

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