SOLUTION: The population of Gondor is 3020 and is dropping by 12 people per year. The population of Shire is 824 and is increasing by 5 hobbits per year. How long until Gondor and Shire have

Question 165797: The population of Gondor is 3020 and is dropping by 12 people per year. The population of Shire is 824 and is increasing by 5 hobbits per year. How long until Gondor and Shire have the same population?
Found 2 solutions by Fombitz, MRperkins:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
"Gondor is 3020 and is dropping by 12 people per year"

"Shire is 824 and is increasing by 5 hobbits per year"

Set the two populations equal to each other and solve for Y.

.
.
.
It's not an exact year, around the second month in the 129th year.
Around then, each village will have 1470 inhabitants.

Answer by MRperkins(300) (Show Source): You can put this solution on YOUR website!
Population of Gondor=3020-12x
Population of Shire=824+5x
.
We want to know when they will equal the same population so set the two equations = to each other
so...
.

Get all the x's on the same side
since we have -12x on the left, add 12x to both sides (whatever you do on one side you have to do to the other side)
.
you get:
combine like terms
.
you get:
subtract 824 from both sides
.
you get:
combine like terms
.
you get:
divide each side by 17
.
you get
This reduces to
and the decimal is 129.1764 or 129.18 years
.
Therefore the populations of Gondor and Shire will be equal in 129.18 years.
.
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