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Math Help - A word problem

  1. #1
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    A word problem

    I've always had a problem with word problems...

    1)A baseball team is trying to determine what price to charge for tickets. At a price of $10 per ticket, it averages 45,000 people per game. For every increase of $1, it loses 5,000 people. Everyone person at the game spends an average of $5 on concessions. What price per ticket should be charged in order to maximize revenue?

    2) The volume of a rectangular box with a square base remains constant at 400 cm^3 as the area of the base increases as a rate of 15cm^3/sec. Find the rate at which the height of the box is decreasing when each side of the base is 19 cm long. (don't round answer)
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  2. #2
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    Hello, dizizviet!

    Here's the first one . . .


    1) A baseball team is trying to determine what price to charge for tickets.
    At a price of $10 per ticket, it averages 45,000 people per game.
    For every increase of $1, it loses 5,000 people.
    Everyone person at the game spends an average of $5 on concessions.
    What price per ticket should be charged in order to maximize revenue?

    Let x = number of $1 increases in the price of ticket.

    They will charge (10 + x) dollars per ticket.

    For each x, there are 5000x fewer ticket sales.
    . . They will sell: . (45000 - 5000x) tickets.

    So (45000-5000x) tickets are sold at (10+x) dollars each.

    The revenue from ticket sales is: . R_1 \;=\;(10+x)(45000-5000x) dollars.


    The same (45000-5000x) ticketholders will spend $5 each on concessions.

    The revenue from concessions is: . R_2 \;=\;5(45000-5000x) dollars.


    Hence, the Total Revenue is: . R \;=\;(10+x)(45000-5000x) + 5(45000-5000x) dollars.

    . . and that is the function we must maximize.

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