Question 947470


let the present ages of a husband be {{{x}}} and of a wife  {{{y}}}

The present ages of a husband and wife are in the ratio of seven to six, 

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

and five years ago the ratio was six to five. 

{{{(x-5)/(y-5)=6/5}}}............eq.2

to find their ages now, solve this system:

{{{x/y=7/6}}}............eq.1
{{{(x-5)/(y-5)=6/5}}}............eq.2
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start with {{{x/y=7/6}}}............eq.1 and solve for {{{x}}}


{{{x=(7/6)y}}} ....substitute in eq.2

{{{((7/6)y-5)/(y-5)=6/5}}}............eq.2..solve for {{{y}}}


{{{((7/6)y-5)/(y-5)=6/5}}} cross multiply

{{{5((7/6)y-5)=6(y-5)}}}

{{{(35/6)y-25=6y-30}}}

{{{35y/6=6y-30+25}}}

{{{35y=(6y-5)6}}}

{{{35y=36y-30}}}

{{{30=36y-35y}}}

{{{30=y}}}

or {{{y=30}}}

now find {{{x}}}

{{{x=(7/6)y}}} 
{{{x=(7/6)30}}} 

{{{x=(7/cross(6)1)cross(30)5}}} 

{{{x=7*5}}} 

{{{x=35}}} 

so, the present ages of a husband and wife are:

  a husband is {{{35}}} 
a wife is  {{{30}}}

check  the ratio: {{{35/30=7/6}}}  =>{{{1.166666666666667=1.166666666666667}}} => true

five years ago a husband was {{{35-5=30}}}  and wife {{{30-5=25}}}

check  the ratio: {{{30/25=6/5}}} =>{{{1.2=1.2}}} => true