SOLUTION: I really need help trying to make an equation out of this problem. I am having a really hard time turning a word problem into an equation. I am not asking for the answer just help

Question 164306: I really need help trying to make an equation out of this problem. I am having a really hard time turning a word problem into an equation. I am not asking for the answer just help making an equation!! Thank you very much!!! Kathy Gafford
When will Johnson be twice as wealthy as Smith if each has $4000 now and if their estates are increasing at the annual rates of $400 for Smith and $1,200 for Johnson?
Found 2 solutions by stanbon, aka042:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
When will Johnson be twice as wealthy as Smith if each has $4000 now and if their estates are increasing at the annual rates of $400 for Smith and $1,200 for Johnson?
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Smith value: S(x) = 4000 + 400x, where x is the number of years.
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Johnson value: J(x) = 4000 + 1200x, where x is the number of years.
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EQUATION:
Johnson value = 2(Smith value)
4000+1200x = 2(4000+400x)
4000 + 1200x = 8000 + 800x
4000 = 400x
x = 10 years
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Cheers,
Stan H.

Answer by aka042(26) (Show Source): You can put this solution on YOUR website!
Let's let n indicate the number of years that pass, S indicate Smith's estate, and J indicate Johnson's estate.

Both Smith and Johnson start at $4000. So with this information, we can write and . 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 and .

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 . We can now substitute our two equations for S and J as follows: . Now just solve for n!
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