talaangoshtari wrote:The population of a certain town increases by 50 percent every 50 years. If the population in 1950 was 810, in what year was the population 160?
A. 1650
B. 1700
C. 1750
D. 1800
E. 1850
The population increases by 50% every 50 years.
We can PLUG IN THE ANSWERS, which represent the year in which the population was 160.
When the correct answer choice is plugged in, the population in 1950 will be 810.
Answer choice D: 1800
Population in 1850 = 160 + 50% of 160 = 160+80 = 240.
Population in 1900 = 240 + 50% of 240 = 240+120 = 360.
Population in 1950 = 360 + 50% of 360 = 360+180 = 540.
Too small.
Notice that the population must increase by 50% just ONCE MORE to reach 810.
540 + 50% of 540 = 540+270 = 810.
Since one more 50% increase is needed, the correct answer choice must be 50 years earlier than answer choice D.
The correct answer is
C.
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