A travel agent offers a vacation plan which costs z dollars

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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.
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by [email protected] » Fri Nov 03, 2017 1:34 pm
Hi AAPL,

We're told that the total cost of a vacation plan is Z dollars for the FIRST day and Z/6 dollars for EACH additional day. We're asked for the cost of a vacation of Y days, where y>1. This question can be solved by TESTing VALUES.

IF...
Z=6
Then the first day costs $6 and each additional day costs 6/6 = $1.
Y=2
Then the total cost is $6 + 1($1) = $7

Thus, we're looking for an answer that equals 7 when we plug in Z=6 and Y=2. There's only one answer that matches...

Final Answer: D

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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.
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by Scott@TargetTestPrep » Sun Nov 03, 2019 7:37 pm
AAPL wrote: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.
A vacation of y days costs:

z + z/6(y - 1)

z + (zy - z)/6

6z/6 + (zy - z)/6

(zy + 5z)/6

Answer: D

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