Question 1124900
let's father's age be {{{x}}} and son's age {{{y}}}

if father is {{{24}}} years older than the son, we have

 {{{x=y+24}}}...eq.1


 if the ratio of their age is {{{5:2}}}, we have

{{{x:y=5:2}}}....eq.2.....solve or {{{x}}}

{{{2x=5y}}}

{{{x=5y/2}}}....eq.2a

from eq.1 and eq.2a we have

{{{5y/2=y+24}}}...solve or {{{y}}}

{{{5y=2y+48}}}

{{{5y-2y=48}}}

{{{3y=48}}}

{{{y=48/3}}}

{{{highlight(y=16)}}}

find {{{x}}}:

{{{x=y+24}}}...eq.1

{{{x=16+24}}}

{{{highlight(x=40)}}}

so, father is {{{highlight(40)}}} years old, and son is {{{highlight(16)}}} years old


check the ratio:

{{{x:y=5:2}}}

{{{40:16=5:2}}}...simplify left side
{{{5:2=5:2}}} -> which confirms our solution