Question

In 1990, the population of the Midwest was about 60 million. During the 1990s, the population of this area increased an average of about 0.4 million per year. The population of the West was about 53 million in 1990. The population of this area increased an average of about 1 million per year during the 1990s. Assume that the rate of growth of these areas remains the same. Estimate when the population of the West would be equal to the population of the Midwest answer key

Answer 1

Answer:

The population of both Midwest and West will be equal after 11 years and 8 months.

Step-by-step explanation:

It is provided that in 1990 the population of Midwest was 60 million and that of West was 53 million.

The average increase in population of Midwest areas is 0.4 million/year and in case of west areas it is 1 million/year.

The expression representing the population of Midwest in x years is:

$P_{M}=60 + 0.40x$

The expression representing the population of West in x years is:

$P_{W}=53 + 1.00x$

Compute the value of x such that the population of both Midwest and West are same as follows:

$P_{M}=P_{W}\\60+0.40x=53+1.00x\\1.00x - 0.40x=60-53\\0.60x=7\\x=\frac{7}{0.60}\\x=11\frac{2}{3}$

So after $11\frac{2}{3}$ years or 11 years and 8 months the population of both Midwest and West will be equal.