Question

Please help!! I don't know how to set this up!!

A 2002 Loyola University of Chicago study showed a marked decrease in blue-eyed Americans. About one-half of Americans were born in 1900 with blue eyes. By 1950 that number had dropped to one-third. The 2000 Census states that only about 1 of every 6 Americans had blue eyes. If the rate of decrease continues at the same rate as the prior 50 years, what fraction of people will be born with blue eyes by the year 2050?

Answer 1

I can't help notice the upper-right-corner picture of "no calculators allowed".

the rate for the prior 50 years has been that,

1950 1/3 of americans were blue-eyed.

2000 1/6 of americans were blue-eyed

so in 50 years, it went from 1/3 to 1/6, well, low and behold, 1/6 is half of 1/3

`\bf \cfrac{\quad (1)/(3)\quad }{2}\implies \cfrac{\quad (1)/(3)\quad }{(2)/(1)}\implies \cfrac{1}{3}\cdot \cfrac{1}{2}\implies \cfrac{1}{6}`

so, in 2050, namely in 50 years from 2000, we can expect that it'll drop to another half then,

`\bf \cfrac{\quad (1)/(6)\quad }{2}\implies \cfrac{\quad (1)/(6)\quad }{(2)/(1)}\implies \cfrac{1}{6}\cdot \cfrac{1}{2}\implies \cfrac{1}{12}`