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
[tex]C_1=20+2x[/tex] ...(i)
Book club B charges $10 for membership and $3 per book rental. So, the total cost is
[tex]C_2=10+3x[/tex] ...(ii)
Equating (i) and (ii), we get
[tex]10+3x=20+2x[/tex]
[tex]3x-2x=20-10[/tex]
[tex]x=10[/tex]
The total cost is
[tex]C_1=20+2(10)[/tex]
[tex]C_1=20+20[/tex]
[tex]C_1=40[/tex]
Therefore, the total cost at both book clubs are same for 10 rental books and that cost is $40.
