Question 1183266

let man's age be {{{x}}} and wife's age {{{y}}}

 if a man is six years older than his wife, we have

{{{x=y+6}}}.....eq.1


if six years ago the ratio of their ages was {{{7:6 }}}, we have


{{{(x-6)/(y-6)=7/6}}} .........cross multiply

{{{6(x-6)=7(y-6)}}}

{{{6x-36=7y-42}}}..........solve for {{{x}}}

{{{6x=7y-42+36}}}

{{{6x=7y-6}}}

{{{x=7y/6-1}}}........eq.2


from eq.1 and eq.2 we have

{{{ y+6=7y/6-1}}}........solve for {{{y}}}

{{{ 1+6=7y/6-y}}}

{{{ 7=7y/6-6y/6}}}

{{{ 7=y/6}}}

{{{ 7*6=y}}}

{{{y=42}}}


go to

{{{x=y+6}}}.....eq.1, substitute {{{y}}}


{{{x=42+6}}} 

{{{x=48}}} 



 their present ages:

man is {{{48}}} years old

his wife is {{{42}}} years old