Question 240593
This requires several steps, so fasten your seatbelts!  :)
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If Tom was twice John's age 4 years ago, then we can say that 4 years ago:
x = John
2x = Tom
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However, this was four years ago.  Thus, in order to bring them to their current ages, we will say:
x+4 = John
2x+4 = Tom
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Now, the problem tells us that 4 years from now John will be 3/4 Tom's age.  So, four years from now:
John will be = (x+4)+4
Tom will be = (2x+4)+4
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Now we are ready to write our equation for when John will be 3/4 Tom's age:
John+4 = (3/4)Tom+4
{{{(x+4+4)=(3/4)(2x+4+4)}}}
{{{x+8=(3/4)(2x+8)}}}
{{{x+8=(3*2x/4)+(3*8/4)}}}
{{{x+8=(3*1x/2)+(24/4)}}}
{{{x+8=(3x/2)+6}}}
{{{x-(3x/2)=6-8}}}
{{{2x/2-3x/2=-2}}}
{{{-x/2=-2}}}
{{{x=-2*(-2)}}}
{{{x=4}}}
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Now figure out their ages (today):
Remenber x+4 is John and 2x+4 is Tom... so,
4+4=8 ...John
2*4+4 = 8+4 = 12 ...Tom
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Check that John will be 3/2 Tom's age in 4 years.
Remember x+4+4 corresponds to John and [(3/2)(2x+4)] to Tom.
x+4+4=(3/4)(2x+4+4) ??
4+4+4=(3/4)(2*4+4+4)
12=(3/4)(16)
12=12
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Done!  :)