Question 165797
Population of Gondor=3020-12x
Population of Shire=824+5x
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We want to know when they will equal the same population so set the two equations = to each other
so...
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{{{3020-12x=824+5x}}}
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)
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you get:{{{3020-12x+12x=824+5x+12x}}}
combine like terms
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you get:{{{3020=824+17x}}}
subtract 824 from both sides
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you get:{{{3020-824=824+17x-824}}}
combine like terms
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you get:{{{2196=17x}}}
divide each side by 17
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you get {{{2196/17=17x/17}}}  
This reduces to 
{{{2196/17=x}}} and the decimal is 129.1764 or 129.18 years
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Therefore the populations of Gondor and Shire will be equal in 129.18 years.
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