The total cost for a member who buys x hardcover books in a year is the same for Plan A and Plan B. What is the value o…

To find the number of hardcover books, x, for which the total cost of the two plans is equal, we first need to write an expression for the total cost of each plan.

Let C_A be the total cost of Plan A and C_B be the total cost of Plan B.

For Plan A, the cost is the $20 yearly fee plus $12 for each of the x books: C_A = 20 + 12x.

For Plan B, the cost is the $50 yearly fee plus $9 for each of the x books: C_B = 50 + 9x.

The question asks for the value of x when the costs are equal, so we set the two expressions equal to each other:

20 + 12x = 50 + 9x

To solve for x, we can first subtract 9x from both sides of the equation:

20 + 3x = 50

Next, subtract 20 from both sides:

3x = 30

Finally, divide both sides by 3:

x = 10

So, the total cost is the same for both plans when a member buys 10 hardcover books.

A is incorrect. This is the difference between the per-book prices ($12 - $9 = $3).

C is incorrect. This is the difference between the yearly fees ($50 - $20 = $30).

D is incorrect. This is the total cost for either plan when x=10 books are purchased ($20 + 12(10) = $140), not the number of books.