A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each which is to have either 80 ft or 100 ft of lake frontage. If 1/9 of the lots are to have 80 ft of lake frontage and the remaining 40 lots are to have 100 feet of frontage each, what is the value of x?

(ps. I have the answer..just need help with the process)

Question

A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each which is to have either 80 ft or 100 ft of lake frontage.  If 1/9 of the lots are to have 80 ft of lake frontage and the remaining 40 lots are to have 100 feet of frontage each, what is the value of x?

(ps. I have the answer..just need help with the process)

gw2011 · Answer

I got an answer of x = 4400 feet of lake frontage.  If this is correct, this is how I got the answer:  since 1/9 of the lots are to have 80 ft, then the 40 lots of 100 ft each represents 8/9.  Taking a proportion to find how many lots are represented by 1/9 you do:

(8/9)/40=(1/9)/x  Cross multiplying this you get:

(8/9)x=(1/9)(40)
x=(1/9)(40)(9/8)
x=5 lots

(40 lots)(100 ft)=4000 ft
(5 lots)(80 ft)=400 ft

Total x=4400 ft

anonymous · Answer

Where did you get 8/9 from? Pls explain.

gw2011 · Answer

Since 1/9 represents 80 feet, then 8/9 is the remaining amount (the 1/9 + 8/9 gives 9/9 = 1 = 100%).