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# A travel agent offers a vacation plan which costs z dollars for the fi

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Math Expert
Joined: 02 Sep 2009
Posts: 59756
A travel agent offers a vacation plan which costs z dollars for the fi  [#permalink]

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17 Oct 2019, 00:12
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Difficulty:

45% (medium)

Question Stats:

55% (01:53) correct 45% (01:40) wrong based on 44 sessions

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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. yz/6
B. yz/3
C. (yz + 6z)/6
D. (yz + 5z)/6
E. (y^2z + 5yz + z^2)/3

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Re: A travel agent offers a vacation plan which costs z dollars for the fi  [#permalink]

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17 Oct 2019, 10:47
Bunuel 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. yz/6
B. yz/3
C. (yz + 6z)/6
D. (yz + 5z)/6
E. (y^2z + 5yz + z^2)/3

let y=2
so total cost ; z+z/6 ; 7z/6
substitute value of y =2 in given answer options
IMO D: gives 7z/6
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Joined: 12 Sep 2015
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A travel agent offers a vacation plan which costs z dollars for the fi  [#permalink]

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17 Oct 2019, 10:49
Top Contributor
Bunuel 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. yz/6
B. yz/3
C. (yz + 6z)/6
D. (yz + 5z)/6
E. (y^2z + 5yz + z^2)/3

One approach is to look for a pattern

1 day: cost = $$z$$ dollars

2 days: cost = $$z + \frac{z}{6}$$ dollars

3 days: cost = $$z + \frac{z}{6}+ \frac{z}{6}$$ dollars

4 days: cost = $$z + \frac{z}{6}+\frac{z}{6}+\frac{z}{6}$$ dollars

Notice that the number of times we add z/6 is 1 less than the number of vacation days
.
.
.
y days: cost = $$z + (y-1)(\frac{z}{6})$$ dollars

Check answer choices....$$z + (y-1)(\frac{z}{6})$$ is not an option. So, we must simplify this expression.

Take: $$z + (y-1)(\frac{z}{6})$$

Rewrite $$z$$ as $$\frac{6z}{6}$$ to get: $$\frac{6z}{6} + \frac{(y-1)z}{6}$$

Simplify: $$\frac{6z}{6} + \frac{yz-z}{6}$$

Simplify: $$\frac{6z+(yz-z)}{6}$$

Simplify: $$\frac{5z+yz}{6}$$

Cheers,
Brent
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Re: A travel agent offers a vacation plan which costs z dollars for the fi  [#permalink]

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19 Oct 2019, 22:07
$z - First day$ z/6 - For each additional day
z+z/6(y-1) = 5z/6 + zy/6 = 1/6(5z+zy) --- D is the correct ans.
Re: A travel agent offers a vacation plan which costs z dollars for the fi   [#permalink] 19 Oct 2019, 22:07
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