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)

Answer 1

if 1/9 of the lots have 80 ft of lake frontage, then 8/9 of the lots is 40 lots.
so...8/9 of what = 40
8/9n = 40
n = 40 * 9/8
n = 360/8
n = 45

so there are a total of 45 lots

1/9 (45) = 45/9 = 5...there are 5 lots that have 80 ft lake frontage = (5 * 80) = 400 ft lake frontage

8/9 (45) = 360/9 = 40...there are 40 lots that have 100 ft lake frontage = (100 * 40) = 4000 ft lake frontage

for a total of 4400 ft total lake frontage

Answer 2

Answer: if 1/9 of the lots have 80 ft of lake frontage, then 8/9 of the lots is 40 lots.

so...8/9 of what = 40

8/9n = 40

n = 40 * 9/8

n = 360/8

n = 45

so there are a total of 45 lots

1/9 (45) = 45/9 = 5...there are 5 lots that have 80 ft lake frontage = (5 * 80) = 400 ft lake frontage

8/9 (45) = 360/9 = 40...there are 40 lots that have 100 ft lake frontage = (100 * 40) = 4000 ft lake frontage

for a total of 4400 ft total lake frontage