Question 375011
Let B = bill's age now, T = Tom's age now



So Bill's age 3 yrs ago was {{{B-3}}} and Tom's age 3 yrs ago was {{{T-3}}} 



Since "Bill is 6 years older than Tom", we know that {{{B=T+6}}}



Also, because "Bill's age was four times Tom's age", we know that {{{B-3=4(T-3)}}}



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{{{B-3=4(T-3)}}} Start with the second equation.



{{{T+6-3=4(T-3)}}} Plug in {{{B=T+6}}} (ie replace each 'B' with 'T+6'). So this would be the starting point of the single variable equation you're looking for.



{{{T+6-3=4T-12}}} Distribute.



{{{3+T=4T-12}}} Combine like terms on the left side.



{{{T=4T-12-3}}} Subtract {{{3}}} from both sides.



{{{T-4T=-12-3}}} Subtract {{{4T}}} from both sides.



{{{-3T=-12-3}}} Combine like terms on the left side.



{{{-3T=-15}}} Combine like terms on the right side.



{{{T=(-15)/(-3)}}} Divide both sides by {{{-3}}} to isolate {{{T}}}.



{{{T=5}}} Reduce.



So this means that Tom is 5 yrs old.



Now plug this value into {{{B=T+6}}} to get  {{{B=5+6=11}}}. So {{{B=11}}} which means that Bill is 11 yrs old.



Notice that 3 yrs ago, Bill was 11-3=8 yrs old and Tom was 5-3=2 years old. Also notice that 8 is 4 times 2.



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Jim