Question

Book club A charges $20 for membership and $2 per book rental. Book club B charges $10 for membership and $3 per book rental. For how many movie rentals will the cost be the same at both book clubs? What does that cost?

Answer 1

The cost will be the same at both book clubs when there are 10 movie rentals, and the cost will be $40.

Step-by-step explanation:

To find the number of movie rentals for which the cost is the same at both book clubs, we can set up two equations and solve for the number of rentals that satisfy both equations. Let x be the number of movie rentals:

Cost at Book Club A = $20 + $2 * x

Cost at Book Club B = $10 + $3 * x

We want to find x when the cost at both book clubs is equal, so we can set up the equation:

$20 + $2 * x = $10 + $3 * x

Now we can solve for x:

$2 * x - $3 * x = $10 - $20

-$1 * x = $-10

x = 10

So, the cost will be the same at both book clubs when there are 10 movie rentals, and the cost will be $40.

Answer 2

Given:

Book club A charges $20 for membership and $2 per book rental.

Book club B charges $10 for membership and $3 per book rental.

To find:

The number of books for which the cost be the same at both book clubs.

Solution:

Let x be the number of books.

Book club A charges $20 for membership and $2 per book rental. So, the total cost is

`C_1=20+2x` ...(i)

Book club B charges $10 for membership and $3 per book rental. So, the total cost is

`C_2=10+3x` ...(ii)

Equating (i) and (ii), we get

`10+3x=20+2x`

`3x-2x=20-10`

`x=10`

The total cost is

`C_1=20+2(10)`

`C_1=20+20`

`C_1=40`

Therefore, the total cost at both book clubs are same for 10 rental books and that cost is $40.