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# A developer has land that has x feet of lake frontage. The l

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A developer has land that has x feet of lake frontage. The l [#permalink]  24 Jan 2017, 07:44
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Question Stats:

76% (01:01) correct 23% (03:12) wrong based on 26 sessions

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
[Reveal] Spoiler: OA

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Re: A developer has land that has x feet of lake frontage. The l [#permalink]  28 Jan 2017, 07:37
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Explanation

We start by finding the number of lots: $$\frac{1}{9}$$ of the total lots + 40 lots = total lots and let total lots = t
$$\frac{1}{9} t + 40 = t$$ → $$(9)\times \frac{1}{9} \times t + (9) \times 40 = 9t$$ → $$1t + 360 = 9t$$

Hence $$360 = 8t$$ → $$45 = t$$.

If there are 45 total lots and 40 of them have 100 feet of frontage, then 5 of them have 80 feet of frontage. Determine the total frontage:

40 have 100 feet: 40 × 100 = 4000
5 have 80 feet: 5 × 80 = 400

Total Frontage = 4000 + 400 = 4400.

Hence option D is correct.
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Re: A developer has land that has x feet of lake frontage. The l [#permalink]  08 Nov 2018, 07:26
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Alternate approach

For finding the value of t we can equate

$$\frac{8}{9} t =40$$ (because from the question if $$\frac{1}{9}$$ lots are of $$80$$ ft then the rest $$\frac{8}{9}$$ t must be of 100 feet)
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Re: A developer has land that has x feet of lake frontage. The l   [#permalink] 08 Nov 2018, 07:26
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