Question 292219
Two years ago John was three times as old as Frank. Five years from now John will be twice as old as Frank. What is the sum of their ages right now?
how do you figure this out?  thanks

Two years ago John was 
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<font color = "red">J-2</font>, which was <font color = "red">=</font> to
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three times
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that's <font color = "red">3*</font>
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as old as Frank. 
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(was two years ago), which was <font color = "red">(F-2)</font>.

So following everything in red above,
we have this equation:

<font color = "red">J-2 = 3*(F-2)</font>
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Five years from now John will be 
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<font color = "green">J+5</font>, which <font color = "green">=</font>
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twice as old 
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(that's <font color = "green">2*</font>)
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as Frank.
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(as Frank will be five years from now), 
which will be <font color = "green">(F+5)</font> 

So following everything above in green, 
we have this equation:

<font color = "green">J+5 = 2*(F+5)</font>

So we have this system:

<font color = "red">J-2 = 3*(F-2)</font>
<font color = "green">J+5 = 2*(F+5)</font>

Can you simplify that system and 
solve it?  If not post again asking how.

J=11, F=5

So John is 11 and Frank is 5

Checking:
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Two years ago John was 
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(9, which was) 
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three times as old as Frank. 
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(who was then 3) 
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Five years from now John will be 
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(16, which will be) 
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twice as old as Frank. 
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(who will be 8).
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What is the sum of their ages right now?
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Add 11 + 5 and get 16. 

Edwin</pre></font></b>