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19 November, 03:37

An advertiser rents a rectangular billboard that is 21.5 ft wide and 13 ft tall. The rent is $12 per square foot. For a billboard three times as tall, the advertiser has to pay $30,186. Is this reasonable? Explain.

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Answers (2)
  1. 19 November, 04:08
    0
    If the cost is only variable, the proportion of the cost is wrong.

    The proportionated cost should be of $10,062

    Explanation:

    Giving the following information:

    An advertiser rents a rectangular billboard that is 21.5 ft wide and 13 ft tall. The rent is $12 per square foot. For a billboard three times as tall, the advertiser has to pay $30,186.

    First, we need to calculate the cost of the first billboard:

    Square foot = 21.5*13 = 279.5sq

    Total cost = 279.5*12 = $3,354

    Now, a billboard 3 times as tall:

    Square foot = 21.5 * (13*3) = 838.5

    Total cost = 838.5*12 = 10,062

    If the cost is variable, the proportion of the cost is wrong.

    The proportionated cost should be of $10,062
  2. 19 November, 05:12
    0
    No; when the height is tripled, the area is also tripled.

    Explanation:

    Use the formula for area of a rectangle to find the area of the smaller billboard.

    A=bh

    Substitute 21.5 for b, 13 for h, and simplify.

    A = (21.5) (13) = 279.5 ft2

    Therefore, the area of the smaller billboard is 279.5 ft2.

    Use the formula for area of a rectangle to find the area of the billboard with triple height.

    A=bh

    Substitute 21.5 for b, 3⋅13 for h, and simplify.

    A = (21.5) (3⋅13) = (21.5) (39) = 838.5 ft2

    Therefore, the area of the billboard with triple height is 838.5 ft2.

    Notice that 838.5=3 (279.5), which is 3 times the area of the smaller billboard.

    So, the area has changed by a factor of 3.

    Therefore, when the height is tripled, the area is also tripled.

    It is given that the rent is $12 per square foot.

    Calculate the rent of the billboard of 279.5 ft2.

    12⋅279.5=3,354

    Therefore, for the billboard of 279.5 ft2 the advertiser has to pay $3,354.

    It is also given that for the billboard with triple height the advertiser has to pay $30,186.

    Notice that $30,186=9 ($3,354), which is 9 times the rent for the smaller billboard.

    So, the rent has changed by a factor of 9.

    Since the area is tripled, the rent $30,186 for a billboard three times as tall is not reasonable.

    Therefore, this rent is not reasonable.
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Home » Business » An advertiser rents a rectangular billboard that is 21.5 ft wide and 13 ft tall. The rent is $12 per square foot. For a billboard three times as tall, the advertiser has to pay $30,186. Is this reasonable? Explain.
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