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Bunuel
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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Bunuel
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

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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