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

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

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 D

Cheers,
Brent

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