Question

A chef self-publishes a cookbook and finds that the number of books she can sell per month varies inversely as the price of the book. The chef can sell 200 books per month when the price is set at $6 per book. How many books would she expect to sell per month if the price were $8? A) 150 books per month B) 100 books per month C) 75 books per month D) 50 books per month

Answer 1

Using the inverse variation formula, we determined that the chef can sell 150 books per month at a price of $8 per book, which corresponds to option A.

Step-by-step explanation:

The student's question involves inverse variation, which means that one value decreases as another value increases and vice versa. Given the information that the chef can sell 200 books at $6 each, we can set up an inverse variation formula where the number of books sold (x) is inversely proportional to the price of the book (p), such that x ∙ p = k, where k is the constant of variation. We know x = 200 books and p = $6, so we can solve for k:

200 ∙ 6 = k

k = 1200

Now we can find how many books the chef can sell at $8:

­x = ­k / p

­x = 1200 / 8

­x = 150

Therefore, the chef would expect to sell 150 books per month if the price were $8, corresponding to option A.

Answer 2

The chef would expect to sell 150 books per month if the price were $8.

Step-by-step explanation:

To solve this problem, we can use the concept of inverse variation. In inverse variation, two variables are inversely proportional to each other when their product is a constant. Let's represent the number of books sold per month as y and the price of the book as x. Based on the given information, we have the following relationship: y * x = k, where k is a constant.

We know that when the price is set at $6 per book, the chef can sell 200 books per month. Substituting these values into the equation, we have 200 * 6 = k. Therefore, the constant k is 1200.

Now, we can use the value of k to find the number of books the chef would expect to sell per month if the price were $8. We set up the equation as follows: y * 8 = 1200. Solving for y, we find y = 150. Therefore, the chef would expect to sell 150 books per month if the price were $8.