Question 951641

let Emily's age be {{{x}}} and her  aunt Ingrid {{{y}}}

if Emily is one quarter or {{{1/4}}} the age of aunt Ingrid, then we have:

{{{x=(1/4)y}}} ....eq.1

if their total age is {{{60}}}, then we have:
{{{x+y=60}}}.......eq.2 

to find out how old is Emily, solve this system:

{{{x=(1/4)y}}} ....eq.1
{{{x+y=60}}}.......eq.2 
---------------------------substitute {{{(1/4)y}}} for {{{x}}} from eq.1 in eq.2

{{{(1/4)y+y=60}}}.......eq.2 ....solve for {{{y}}}

{{{y/4+4y/4=60}}}

{{{5y/4=60}}}

{{{5y=60*4}}}

{{{y=240/5}}}

{{{y=48}}}

now find {{{x}}}

{{{x=(1/4)y}}} ....eq.1

{{{x=(1/cross(4)1)cross(48)12}}} 

{{{highlight(x=12)}}} 

so, Emily is {{{highlight(12)}}} years old