Question

$V\left(t\right)=at+k$
At a certain manufacturing plant, the total number of vacation days, $V\left(t\right)$, an employee has accrued is given by the function above, where $t$ is the number of years the employee has worked at the plant and a and $k$ are constants.Calculate the number of years which Nathan has worked more than Nitin if Nathan has accrued $9$ more holidays than Nitin.

• A. $\frac{9}{a}$
• B. $9-a$
• C. $9+a$
• D. $9a$

Answer 1

The correct option is A $\frac{9}{a}$

Solution:-

Whenever there are variables in the question and in the answers, think Plugging In. Let's say that for Nitin $a=2,t=4$, and $k=10$. Then Nitin's accrued vacation days can be calculated as $V\left(t\right)=2\left(4\right)+10=18$. This means that Nathan has accrued $18+9=27$ vacation days. Because $a$ and $k$ are constants, their values do not change. The number of years that Nathan has worked at the manufacturing plant can therefore be calculated as $27=2t+10$. Solve for $t$ to get $17=2t$or $t=8.5$. Therefore, Nathan has worked $(8.5-4=)4.5$ more years than Nitin. Plug $2$ in for a in the answers to see which answer equals $4.5$.

Hence, $\frac{9}{a}$ is correct answer.