A travel agent offers a vacation plan which costs z dollars

A travel agent offers a vacation plan which costs z dollars for the first day and z/6 dollars for each additional day. How much does a vacation of y days cost, in dollars, where y>1??

$$A.\ \ \frac{yz}{6}$$
$$B.\ \ \frac{yz}{3}$$
$$C.\ \ \frac{(yz+6z)}{6}$$
$$D.\ \ \frac{(yz+5z)}{6}$$
$$E.\ \ \frac{(y^2z+5yz+z^2)}{3}$$

The OA is D.

I don't have clear this PS question. Please, can any expert explain it for me? Thanks.

Hi AAPL,
Let's take a look at your question.

The question states:
"A travel agent offers a vacation plan which costs z dollars for the first day and z/6 dollars for each additional day. How much does a vacation of y days cost, in dollars, where y>1??"

Total days of vacation = y days
Cost of first day of vacation = z dollars
Remaining days after spending z dollars for the first day = (y - 1) days
Cost of each additional day after the first day = z/6
Cost for (y-1) additional days = (y-1)*z/6

Now we can find the total cost of vacation of y days.
Total cost of y days = Cost of first day + Cost of (y-1) additional days
$$=\ z\ +\ \left(y-1\right)\left(\frac{z}{6}\right)$$
$$=\ z\ +\ \frac{\left(y-1\right)z}{6}$$
$$=\ z\ +\ \frac{yz-z}{6}$$
$$=\ \ \frac{6z+yz-z}{6}$$
$$=\ \ \frac{yz-z+6z}{6}$$
$$=\ \ \frac{yz+5z}{6}$$

Therefore, Option D is correct.

Hope it helps.
I am available if you'd like any follow up.