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.

Question

Business

Titus Douglas

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)

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Mariah · Answer 1

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

Ayla Hines · Answer 2

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.