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A developer has land that has x feet of lake frontage. The land is to

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A developer has land that has x feet of lake frontage. The land is to  [#permalink]

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New post 11 Jul 2018, 23:52
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A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 80 feet or 100 feet of Lake Frontage. If (1/9) of the lots are to have 80 feet of frontage each and the remaining 40 lots are to have 100 feet of frontage each, what is the value of x?

(A) 400
(B) 3,200
(C) 3,700
(D) 4,400
(E) 4,760

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Re: A developer has land that has x feet of lake frontage. The land is to  [#permalink]

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New post 12 Jul 2018, 01:50
A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 80 feet or 100 feet of Lake Frontage. If (1/9) of the lots are to have 80 feet of frontage each and the remaining 40 lots are to have 100 feet of frontage each, what is the value of x?

(1/9)ths of the lots are to have 80 feet of frontage each which means remaining lot for 100 feet frontage is [(9-1)/9]X = 8/9
8Y/9 = 40 => Y = 40*9/8 = 5*9 = 45 lot

Remaining lots for 80 Feet are 5 lots.

Total X feet of lake frontage = 80*5 + 40*100 = 400 + 4000 = 4400

Answer D
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A developer has land that has x feet of lake frontage. The land is to  [#permalink]

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New post 12 Jul 2018, 14:56
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Bunuel wrote:
A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 80 feet or 100 feet of Lake Frontage. If (1/9) of the lots are to have 80 feet of frontage each and the remaining 40 lots are to have 100 feet of frontage each, what is the value of x?

(A) 400
(B) 3,200
(C) 3,700
(D) 4,400
(E) 4,760

I. The 20-second method

If there are 40 lots with 100 feet of lake frontage, there are at least
40 lots * \(\frac{100ft}{lot}\) = 4,000 feet of lake frontage

Eliminate A, B, C

Answer D or E? Check remaining feet.

D) 4,400 - 4,000 = 400
E) 4,760 - 4,000 = 760

Each remaining lot is 80 feet. There are no partial lots. The total of remaining feet must be divisible by 80.

D) 400/80 = 5 lots
E) 760/80 = 9.5 lots

Answer D

II. Another approach

Solve for # of lots, then find total feet. We have a counting number for lots.

Let lots with 80 feet of lake frontage be "Small"

Let lots with 100 feet of lake frontage be "Big"

\(x\) = total feet of lake frontage
\(x\) = (# of Small lots * 80 ft) + (# of Big lots * 100 ft)

Small lots = \(\frac{1}{9}\) of all lots

So the rest of the lots = Big = \(\frac{8}{9}\) of all lots
There are 40 Big lots

40 Big = \(\frac{8}{9}\) of total lots
\(\frac{9}{8}*40=45\) total lots

Number of Small lots: (All - Big) = (45 - 40) = 5

Number of Big lots = 40

Total x feet of lake frontage land?

(5 * 80ft) + (40 * 100 ft) = (400 + 4,000)ft = 4,400 ft

Answer D
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