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 methodIf 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 approachSolve 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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