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

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

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New post 17 Oct 2019, 00:12
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

56% (01:53) correct 44% (01:39) wrong based on 43 sessions

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

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

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New post 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: \(\frac{5z+yz}{6}\)

Answer: D

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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New post 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.
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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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