Question 164306
Let's let n indicate the number of years that pass, S indicate Smith's estate, and J indicate Johnson's estate.
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Both Smith and Johnson start at $4000.  So with this information, we can write {{{S = 4000}}} and {{{J = 4000}}}.  Now we see that their estates are increasing at $400 and $1200 respectively.  Another way of saying this is that at a given year n, Smith's estate will have increased by $400*n ($400 per year) and Johnson's will have increased by $1200*n.  So our new equations are {{{S=4000 + 400*n}}} and {{{J = 4000 + $1200*n}}}.
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The problem now wants us to find the number of years that it will take for Johnson to be twice as wealth as Smith.  In our equation form, this is the same as saying {{{J = 2S}}}.  We can now substitute our two equations for S and J as follows: {{{4000 + $1200*n = 2*($4000 + $400*n)}}}.  Now just solve for n!