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# Cottages at a resort are rented for half the summer price in each of

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Math Expert
Joined: 02 Sep 2009
Posts: 55801
Cottages at a resort are rented for half the summer price in each of  [#permalink]

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24 Dec 2018, 23:35
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Difficulty:

75% (hard)

Question Stats:

63% (02:44) correct 37% (02:27) wrong based on 66 sessions

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Cottages at a resort are rented for half the summer price in each of the 3 spring months and one-third the summer price in each of the 6 fall and winter months. If each cottage brings in a total of $3,861 when rented for each of the 12 months of the year, what is the monthly rent for each of the 3 summer months? (A)$297
(B) $397 (C)$594
(D) $702 (E)$858

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Re: Cottages at a resort are rented for half the summer price in each of  [#permalink]

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24 Dec 2018, 23:50
Let the price per month for summer be $x. /hence the price for entire year would be 3x+ \frac{3x}{2}+\frac{6x}{3}= 3861 final equation becomes [fraction][/fraction]13x/2 = 3861 x = 594; thus monthly rent =$594
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Re: Cottages at a resort are rented for half the summer price in each of  [#permalink]

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25 Dec 2018, 08:06
Bunuel wrote:
Cottages at a resort are rented for half the summer price in each of the 3 spring months and one-third the summer price in each of the 6 fall and winter months. If each cottage brings in a total of $3,861 when rented for each of the 12 months of the year, what is the monthly rent for each of the 3 summer months? (A)$297
(B) $397 (C)$594
(D) $702 (E)$858

let summer price be x

we can say
3x/2+2x+3x = 3861

x = 594
IMO C
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Re: Cottages at a resort are rented for half the summer price in each of  [#permalink]

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26 Dec 2018, 02:19
1
Bunuel wrote:
Cottages at a resort are rented for half the summer price in each of the 3 spring months and one-third the summer price in each of the 6 fall and winter months. If each cottage brings in a total of $3,861 when rented for each of the 12 months of the year, what is the monthly rent for each of the 3 summer months? (A)$297
(B) $397 (C)$594
(D) $702 (E)$858

Bunuel
Hello please review the answer choice, it should be C not B..
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Re: Cottages at a resort are rented for half the summer price in each of  [#permalink]

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26 Dec 2018, 03:50
Archit3110 wrote:
Bunuel wrote:
Cottages at a resort are rented for half the summer price in each of the 3 spring months and one-third the summer price in each of the 6 fall and winter months. If each cottage brings in a total of $3,861 when rented for each of the 12 months of the year, what is the monthly rent for each of the 3 summer months? (A)$297
(B) $397 (C)$594
(D) $702 (E)$858

Bunuel
Hello please review the answer choice, it should be C not B..

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Re: Cottages at a resort are rented for half the summer price in each of  [#permalink]

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27 Dec 2018, 04:22
Bunuel wrote:
Cottages at a resort are rented for half the summer price in each of the 3 spring months and one-third the summer price in each of the 6 fall and winter months. If each cottage brings in a total of $3,861 when rented for each of the 12 months of the year, what is the monthly rent for each of the 3 summer months? (A)$297
(B) $397 (C)$594
(D) $702 (E)$858

Let the cost of each each month in summer = x......Therefore total cost in summer = 3x

Then, cost of each each month in spring = $$\frac{1}{2}$$x......Therefore total cost in sparing = $$\frac{3}{2}$$x

Also cost of each each month in fall or winter = $$\frac{1}{2}$$x......Therefore total cost in fall and winter = 2x

$$3x + 2x+ \frac{3}{2}x$$= 3861.....multiple by 2

13x = 3861 * 2 ( do not calculate)

Here x Must be Even............eliminate A & B

The unit digit of 3861 * 2 is 2.Therefore scan the other choices to see if 13x gives unit digit 2.....By eyes.....only one answer fits

Re: Cottages at a resort are rented for half the summer price in each of   [#permalink] 27 Dec 2018, 04:22
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