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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 $\$ 25$ 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? $\newline$ Choose $1$ answer: $\newline$ (A) $y=(25+x)(4000-100 x)$ $\newline$ (B) $y=(25-x)(4000+100 x)$ $\newline$ (C) $y=x(4000-100 x)$ $\newline$ (D) $y=4000(25+x)$

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Write two-variable inequalities: word problems

Full solution

Q. 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?

\newline

Choose

1

answer:

\newline

(A)

y=(25+x)(4000-100 x)

\newline

(B)

y=(25-x)(4000+100 x)

\newline

(C)

y=x(4000-100 x)

\newline

(D)

y=4000(25+x)

Ticket Price Relationship: For every $\$1$ increase in ticket price, the number of tickets sold decreases by $100$ . So if the ticket price increases by $x$ dollars, the new ticket price is $\$25 + x$ .
New Tickets Sold Calculation: The new number of tickets sold would be $4000 - 100x$ because for each dollar increase, $100$ fewer tickets are sold.
Total Revenue Calculation: To find the total revenue, $y$ , we multiply the new ticket price by the new number of tickets sold: $y = (25 + x)(4000 - 100x)$ .
Correct Function Identification: Check the answer choices to see which one matches our equation. The correct function is $y = (25 + x)(4000 - 100x)$ , which is option (A).

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