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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # A developer has land that has x feet of lake frontage. The l  Question banks Downloads My Bookmarks Reviews Important topics
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A developer has land that has x feet of lake frontage. The l [#permalink]
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Question Stats: 74% (01:27) correct 25% (02:45) wrong based on 58 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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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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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]
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Carcass 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

Side question: Why is this developer so vague with the lake frontage numbers? Seems a little shady if you ask me Here's a super fast approach

GIVEN: ....the remaining 40 lots are to have 100 feet of frontage each
(40)(100 ft) = 4000 ft.
So, the lake frontage must be longer than 4000 ft.
ELIMINATE A, B, and C

Let's check the 2 remaining answer choices...

D) The TOTAL length of the lakefront (aka x) is 4400 feet
4000 feet is comprised of 100-foot lots
4400 - 4000 = 400.
So, the other 400 feet is comprised of 80-foot lots.
This means there are 5 80-foot lots.
Looks okay.

E) The TOTAL length of the lakefront (aka x) is 4760 feet
4760 - 4000 = 760.
So, the other 760 feet is comprised of 80-foot lots.
Since 80 feet does not divide into 760 feet, answer choice E is impossible.
ELIMINATE E

By the process of elimination, the correct answer is E Cheers,
Brent
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Re: A developer has land that has x feet of lake frontage. The l [#permalink]
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Carcass 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

Here,

Let the total Lots be = T
Given,
$$\frac{1}{9} * T$$ will have 80 feet frontage

so the remaining lots = $$1 - \frac{1}{9} = \frac{8}{9}$$ will have 100 feet frontage

As per ques,

remaining lots is 40 - they have 100 feet frontage.

or $$\frac{8}{9} *T = 40$$

or $$T = 45$$ lots.

Therefore $$40$$ Lots will have = $$40 * 1000 = 4000$$ feet frontage.

Now,

$$\frac{1}{9}$$of Total Lots = $$\frac{1}{9} * 45 = 5$$ lots

These $$5$$ lots will have = $$5 * 80 = 400$$feet frontage

Hence Total feet = $$4000 + 400 = 4400$$
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