SOLUTION: Two towns, Morganville and Crowley, had the same population in a given year. Morganville's population increases by 270 people each year, and Crowley's population increases by 120 p

Question 1097346: Two towns, Morganville and Crowley, had the same population in a given year. Morganville's population increases by 270 people each year, and Crowley's population increases by 120 people each year. In 2010, there are 3,750 people in Morganville and 3,000 people in Crowley. In what year did the two towns have the same population.
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
You are given 2 straight lines and the slopes of
those lines.
Let = the population of Morganville for
any given year
Let = population of Crowley for any given year
Ley = the number of the year starting with
2010 is
--------------------------------------------------
For Morganville in 2010, you are given the point
( 0, 3750 )
The slope for Morganville is people/yr

The equation is

---------------------------
For Crowley, the point is:
( 0, 3000 )
The slope is people/yr

The equation is:

--------------------------
Find when

Since 2010 means then
2010 - 5= 2005
In 2005 the populations were the same
-------------------------------------
check:
Here are the plots of the lines:

Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!
Two towns, Morganville and Crowley, had the same population in a given year. Morganville's population increases by 270 people each year, and Crowley's population increases by 120 people each year. In 2010, there are 3,750 people in Morganville and 3,000 people in Crowley. In what year did the two towns have the same population.

Let population when it was the same in both towns be P,
Let number of years since they were the same, be y
Then for Morganville in 2010, we get: P = 3,000 - 270y
And, for Crowley in 2010, we get: P = 3,750 - 120y
It then follows that: 3,000 - 270y = 3,750 - 120y
- 270y + 120y = 3,750 - 3,000
- 150y = 750

As - 5 indicates 5 years prior to 2010, then they had the same population in:
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