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GRE - Quantitative Reasoning - Geometry

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 h

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

let the total number of lots be t

given 1/9th of total number of lots are 80ft

thus (1-1/9)th of total number of lots will be 100 ft = 40

(1 - 1/9)*t = 40

8/9 * t = 40

t = 40*9/8 = 45

Number of lots with 80ft frontage = 1/9 * 45 = 5

Number of lots with 100ft frontage = 40

Total lake frontage = 80*5 + 40*100 =400 + 4000 = 4400

Option D is correct