SOLUTION: 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 t

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: 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 t      Log On


   



Question 1109525: 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. Find the equation of the system and estimate when the population of
the West would be equal to the population of the Midwest.

Found 2 solutions by Boreal, josmiceli:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Midwest population is 60+0.4x, where x is number of years after 1990
West population is 53+x
they are equal when 53+x=60+0.4x
0.6x=7
x=11 2/3 years or August 2002.
Midwest will be 64.67 million
West will be 64.67 million

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You are given a point and the slope
for both MW and W populations
----------------------------------
For MW:
( 0, 60 )
+m+=+.4+
---------------
For W:
( 0, 53 )
+m+=+1+
---------------
Time in yrs is plotted on the horizontal axis as +t+
Population in millions is plotted on the vertical axis as +P+
The given points are vertical axis intercepts.
---------------
For MW:
+P+=+.4t+%2B+b+
+60+=+.4%2A0+%2B+b+
+b+=+60+
+P+=+.4t+%2B+60+
For W:
+P+=+1%2At+%2B+b+
+53+=+1%2A0+%2B+b+
+b+=+53+
+P+=+t+%2B+53+
---------------
Set the populations, +P+
equal to eachother
+.4t+%2B+60+=+t+%2B+53+
+.6t+=+7+
+t+=+11.667+
----------------
The populations will be the same in
1990 + 11.667 yrs = 2001 and 8 months
----------------
check:
+P+=+.4%2A11.667+%2B+60+
+P+=+64.667+
and
+P+=+11.667+%2B+53+
+P+=+64.667+
OK