SOLUTION: Boomtown's population of 350,000 increases by 15,000 per year, and Ghostville's population of 200,000 decreases by 10,000 per year. In how many years will Boomtown's population be

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Question 61267This question is from textbook Algebra 1 An Integrated Approach
: Boomtown's population of 350,000 increases by 15,000 per year, and Ghostville's population of 200,000 decreases by 10,000 per year. In how many years will Boomtown's population be five times that of Ghostville? This question is from textbook Algebra 1 An Integrated Approach

Answer by joyofmath(189) About Me  (Show Source):
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Let population of Boomtown, B=350000%2B15000y where y is the number of years into the future.
Let population of Ghostville, G=200000-10000y.
We want to know the value of y where B=5G.
So, B=350000%2B15000y+=+5G+=+5%28200000-10000y%29.
Or, 350000%2B15000y+=+1000000-50000y.
Subtract 350000 from both sides: 15000y+=+650000-50000y.
Add 50000y to both sides: 65000y+=+650000 so y=10.
In 10 years Boomtown will have 5 times as many people as Ghostville.
Verify:
In 10 years B=350000%2B15000%2810%29+=+350000%2B150000+=+500000.
In 10 years G=200000-10000%2810%29+=+200000-100000+=+100000, which is 1/5 of B.