Question

Twelve books cost $59.88 and 21 books cost $104.79. Is there is a constant of proportionality between these purchases? Select the correct answer. A. Yes, each book costs $2.85. B. Yes, each book costs $4.99. C. No, some books cost $2.85 and others $8.73. D. No, there is no constant of proportionality.

Answer 1

The constant k for the two purchases is the same, thus there is a constant of proportionality between the two purchases and each book costs $4.99 (option B).

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Answer 2

There is a constant of proportionality between the two purchases and each book costs $4.99 (option B).

Explanation:

A correspondence relation between two variables is of direct proportionality when the quotient between the corresponding quantities is always the same. This quotient is called the constant of proportionality.

In other words, when dividing any quantity of one of the magnitudes by the one that corresponds to it in the other, the value it gives is always the same. This value is known as the constant of proportionality.

In this case, the constant of proportionality k will relate the number of books bought N and their cost C in the following way:

C=k*N

So k is the price per book.

For the 12 books:

`k=(59.88)/(12)`

k=4.99

And for the 21 books:

`k=(104.79)/(21)`

k=4.99

The constant k for the two purchases is the same, thus there is a constant of proportionality between the two purchases and each book costs $4.99 (option B).