Question

A hostel has automated vending machines for beverages. It needs to be periodically filled. The refilling frequency depends on how many students have rooms near the machine. The company uses the function $f\left(s\right)=\frac{s}{25}+1$, to determine how many times per semester the machine must be refilled (where $s$ is the number of students living within the immediate vicinity on ). How many more times must a vending machine that has $400$ students in the immediate vicinity be refilled compared to one that has $300$ students in the immediate vicinity?

• A. $2$
• B. $4$
• C. $7$
• D. $13$

Answer 1

The correct option is B $4$

$f\left(s\right)=\frac{s}{25}+1$

where, $s$ is the number of students living within the immediate vicinity on

Case I :- refilling frequency of vending machine that has $400$ students in the immediate vicinity.

$f\left(400\right)=\frac{400}{25}+1=16+1=17$

Case II :- refilling frequency of vending machine that has $300$ students in the immediate vicinity.

$f\left(300\right)=\frac{300}{25}+1=12+1=13$

No. of times more a vending machine that has $400$ students in the immediate vicinity be refilled compared to one that has $300$ students in the immediate vicinity = refilling frequency of vending machine that has $400$ students in the immediate vicinity - refilling frequency of vending machine that has $300$ students in the immediate vicinity

$\Rightarrow f\left(400\right)-f\left(300\right)=17-13=4$

Hence, $4$ times more a vending machine that has $400$ students in the immediate vicinity be refilled compared to one that has $300$ students in the immediate vicinity.