Question 187098
The combined population of Marysville and Springfield was 25,000 in 2000.
 By 2005 the population of Marysville had increased by 10%, while Springfield
had increased by 9%. If the total population increased by 2380 people then what
 was the population of each city in 2000?
:
Let s = Springfield population in 2000
Let m = Marysville population in 2000
Then
.09s = Springfield increase by 2005
.1m = Marysville increase by 2005
:
"The combined population of Marysville and Springfield was 25,000 in 2000."
m + s = 25000
or
s = (25000 - m)
:
"By 2005 the population of Marysville had increased by 10%, while Springfield had increased by 9%. If the total population increased by 2380 people"
.1m + .09s = 2380
:
"then what was the population of each city in 2000?"
:
Substitute (25000-m) for s in the above equation:
.1m + .09(25000-m) = 2380
.1m + 2250 - .09m = 2380
.1m - .09m = 2380 - 2250
.01m = 130
m = {{{130/.01}}}
m = 13,000 is the 2000 population of Marysville
then
s = 25000 - 13000
s = 12,000 is the 2000 population of Springfield
;
;
Check solution by finding the amt of increase in 2005
.1(13000) + .09(12000) =
 1300 + 1080 = 2380, confirms our solutions
;
:
did this make sense to you now? Any questions about it?