Question

A magazine company charges $a$ dollars for first month of membership and $b$ dollars per month after that. If a customer has paid $\$108.60$, so far for the service, then the expression which represents the number of months he has subscribed to the service, is

• A. $\frac{108.60}{a+b}$
• B. $\frac{108.60-a}{b}$
• C. $\frac{108.60-a-b}{b}$
• D. $\frac{108.60-a+b}{b}$

Answer 1

Answer: (D)

$\frac{108.60-a+b}{b}$

Let the total number of months of subscription be $x$.

Then, the customer pays '$a$' amount for the first month and '$b$' amount per month for the next $(x-1)$ months.

Then the cost incurred will

$a+b(x-1)=108.60$

$\Rightarrow b(x-1)=108.60-a$

$\Rightarrow x-1=\frac{108.60-a}{b}$

$\Rightarrow x=\frac{108.60-a}{b}+1$

$\Rightarrow x=\frac{108.60-a+b}{b}$.