Question

Use a variation model to solve for the unknown value. An author self-publishes a book and finds that the number of books she can sell per month varies inversely as the price of the book. The author can sell 1500 books per month when the price is set at 8 dollars per book. a. How many books would she expect to sell if the price were 12 dollars? b. How many books would she expect to sell if the price were 15 dollars? c. How many books would she expect to sell if the price were 6 dollars?

Name: Problem 46, Chapter 8: Beginning and Intermediate Algebra
Uploaded: 2021-04-25T23:28:30-08:00
Duration: 2 min 13 s
Channel: Erika Bustos

   Use a variation model to solve for the unknown value.
An author self-publishes a book and finds that the number of books she can sell per month varies inversely as the price of the book. The author can sell 1500 books per month when the price is set at 8 dollars per book.
a. How many books would she expect to sell if the price were 12 dollars?
b. How many books would she expect to sell if the price were 15 dollars?
c. How many books would she expect to sell if the price were 6 dollars?

Beginning and Intermediate Algebra

Julie Miller,Molly… 3rd Edition

Chapter 8, Problem 46

Instant Answer

Solved by Expert Erika Bustos

04/25/2021

Step 1

This can be represented by the equation \(y = \frac{k}{x}\), where \(y\) is the number of books sold, \(x\) is the price of the book, and \(k\) is the constant of variation. Show more…

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Use a variation model to solve for the unknown value. An author self-publishes a book and finds that the number of books she can sell per month varies inversely as the price of the book. The author can sell 1500 books per month when the price is set at 8 dollars per book. a. How many books would she expect to sell if the price were 12 dollars? b. How many books would she expect to sell if the price were 15 dollars? c. How many books would she expect to sell if the price were 6 dollars?

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Key Concepts

Inverse Variation

Inverse variation is a relationship between two variables whereby one variable increases as the other decreases such that the product of the two variables remains constant. This concept is key when modeling situations where the outcome is influenced by the reciprocal of a changing input.

Constant of Proportionality

In an inverse variation model, the constant of proportionality is the fixed value that results from multiplying the two variables together. Once determined using a known pair of values, this constant allows for the calculation of unknown values by maintaining the balance expressed by the inverse relationship.

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