Question 1085934
The ratio of Jonathan’s age to David’s age is {{{6:5}}}. 

let Jonathan’s age be {{{x}}} and David’s age {{{y}}}, then we have

{{{x:y=6:5}}}

{{{5x=6y}}}

{{{x=6y/5}}}....eq.1


In seven years it will be {{{7:6}}}:

{{{(x+7):(y+7)=7:6}}}

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

{{{6x+42=7y+49}}}

{{{6x=7y+49-42}}}

{{{6x=7y+7}}}

{{{x=7y/6+7/6}}}.......eq2

from eq1 and eq2 we have

{{{6y/5=7y/6+7/6}}}......solve for {{{y}}}

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

{{{6y=35y/6+35/6}}}...both sides multiply by {{{6}}}

{{{36y=35y+35}}}

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

{{{highlight(y=35)}}}

now find {{{x}}}

{{{x=6y/5}}}....eq.1

{{{x=(6*35)/5}}}....simplify

{{{x=(6*cross(35)7)/cross(5)1}}}

{{{x=6*7}}}

{{{highlight(x=42)}}}

so,Jonathan’s age is {{{highlight(42)}}} and David’s age is {{{highlight(35)}}}

check the ratios:

{{{x:y=6:5}}}
{{{42:35=6:5}}}
{{{1.2=1.2}}}

in seven years Jonathan’s age will be {{{42+7=49}}}, and David’s age will be  {{{35+7=42}}}

{{{49:42=7:6}}}
{{{1.166666666666667=1.166666666666667}}}